11 C 90. Through what angle has it turned in 10 seconds? cos24 +cos55 +cos125 +cos204 +cos300 =½. Prove that :

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1 Class - XI Maths Assigmet 0-07 Topic : Trigoometry Q If the agular diameter of the moo by 0, how far from the eye a coi of diameter cm be kept to hide the moo? cm Q Fid the agle betwee the miute had of a clock ad the hour had whe the time is 7:0 AM 00 Q The agle i oe regular polygo is to that i aother as : ad the umber of sides i first is twice that i the seco Determie the umber of side of two polygos, Q The umber of sides of two regular polygos are as : ad the differece betwee their agles is Fid the umber of sides of the polygos 0, Q A railway trai is travellig o a circular curve of 00 metres radius at the rate of km/hr C 0 Through what agle has it tured i 0 secods? Q cos +cos +cos +cos0 +cos00 =½ Q7 Prove that si Q Prove that : 7 si si si sec sec ta ta Q Q0 Q Q If A, B, C, D be the agles of a cyclic quardilateral, take i order, prove that cos(0 A)+cos(0 +B)+cos(0 +C) si(0 +D)=0 Prove that : taa taa taa=taa taa taa Prove that : sia=cos(a B)+cosB cos(a B)cosA cosb A A si A Prove that : si si ad, lie betwee 0 ad, prove that ta Q If cos, si Q Prove that : ta70 =ta0 +ta0 Q If ta ( cos )=cot( si ), prove that cos Q If cos cos cos, prove that cos cos cos si si si 0 Q7 Prove that : Q If ta A + ta B=a ad cot A + cot B = b, prove that cot(a B) Q If ta x ta x ta x Q0 If, are two differet values of lyig betwee 0 ad which satisfy the equatio cos + cos si ta cos si a b ta x ta x, the prove that ta x si =, fid the value of si( + ) Q If si + si = a ad cos + cos = b, show that (i) si ab a b ii cos b a b a

2 cos cos cos 0 Q Prove that : cos Q Prove that : cos 0 cos 0 cos 0 cos 0 Q Prove that : si0 si 0 si 0 si 70 Q Prove that : i cos cos si si cos ii cos cos cos cos cos cos cos cos x cos x cos x cot x si x si x si x Q Prove that : Q7 A B cos A cos B SiA si B cot, if is eve Prove that : si A si B cos A cos B 0, if is odd Q Prove that : si si si si si si si Q If Q0 If cosec A + sec A = cosec B + sec B, prove that : ta A ta B cot Q If si A si B,, prove that taa B Q Show that : Q Prove that : Q Prove that (i) cos Q si m,, prove that ta m cos m taa B ii si cos cos sec ta sec ta 7 cos cos cos 7 si si si Prove that : cos A cos A 0 cos A 0 7 Q Prove that : cos cos cos cos Q7 Prove that : cos A cos A cos A cos A cos A Q Prove that : cos A=cosA 0cosA+cosA Q Prove that : cos A cos0 A cos0 A cos A Q0 Prove that : cos A cos 0 A cos 0 A cos A si A si A A B

3 Q Prove that : i cot 7 iii ta ii ta Q Prove that : cos cos si Q Prove that : cos cos cos si Q Prove that : ta ta 0 ta ta 0 ta 0 ta 0 Q Show that Q Prove that : cos ec0 sec 0 ta ta ta cot cot Q7 If ta ta, prove that ta Q If ta cos Q si B cos a b ta, prove that ab a cos b a b cos If cos cos cos,, prove that ta ta ta Q0 If cos cos cos the prove that oe of the values of ta is ta cot cos cos Q If ta p where =, beig acute agle, prove that p cos ec q sec p q q Q Prove that si Q Prove that cos cos lies i [, 0] Q Prove that si si ta0 ta0 +7ta0 = Q Evaluate : cosec +cosec +cosec +cosec Q Prove that : si +si +si +si =+si +si Q7 Prove that : si x si x si x ta 7x ta x cos x cos x cos 7x Q Prove that cos0x + cosx + cosx + cosx = cosx cos x

4 Q Prove that : cos cot 7 Q0 Prove that ta(x y)+ta(y z) + ta(z x)=ta(x y) ta(y z) ta(z x) Q ta ta cos ec Prove that ta ta Q If six+siy=a ad cosx+cosy= Fid the value of ta Q Prove that si si si si Q Prove that cos cos si si cos si Q Show that ta x ever lies betwee & ta x Q Pove that cosx sixsix cosx sixsix cos7x sixsix cos - cos 7 six cosecx cosecx Q7 Prove that Q Determie the smallest positive value of x for which si - cos x y ta(x + 00 )=ta(x+0 )tax ta(x -0 ) Q (x=0 ) Sketch the group of the followig fuctios : i y si iii x ii y=cosx y y x iv y=six+cosx v y= six vi y= cosx vii y=si x Q70 If si si = cos cos +=0, prove that + cot ta = 0 Q7 If cos(a+b)si(c D)=cos(A B) si(c+d), show that taatabtac+tad=0 Q7 Solve cos cos cos Q7 Solve si x sixcosx cosx= Q7 Show that ta ta7 ta +ta =, x= ta = x= ta =

5 Maths Assigmet 0-07 TRIGONOMETRICAL FUNCTIONS AND IDENTITIES Q The value of cos ec 0 sec 0 is equal to si 0 si 0 cos for real values of is Q The maximum value of si Q The miimum value of cos +cos for real values of is Q Q7 x=y x> y If cos 0 - si 0 = p the cos 0 is equal to oe of these 0 0 oe of these x= y p p p p The value of si oe of these 7 si si si si si si is equal to oe of these The value of cos 0 cos r 7 cos cos cos cos is oe of these oe of these oe of these r is equal to The value of si oe of these p p Q 7, x ad ta, x are i AP ad ta, y ad ta, y are also i AP the If ta Q0 - Q Q oe of these The least value of cos -si cos +si + is Q The value of cos ec 0 sec 0 is equal to Q si 0 si 0 si si to terms is equal to 0

6 Q Q Q If ABCD is a covex quadrilateral such that sec A + = 0 the the quadratic equatio whose roots are ta A ad cosec A is x -x+=0 x -x-=0 x +x-=0 oe of these If ABCD is a cyclic quadrilateral such that taa-=0 ad cos B+=0 the the quadratic equatio whose roots are cos C, ta D is x -x-=0 x +x+=0 x -x+=0 oe of these The umber of real solutios of the equatio si(e x)=x+-x is Q Q7 0 ifiite The umber of values of x i the iterval[0,] satisfyig the equatio si x-7si x+=0 is Q 0 0 I a triagle ABC, a=, b=, A=0 The c is the root of the equatio c-c-7=0 c+c+7=0 c-c+7 c+c-7 If the sides a,b,c of a triagle ABC are the roots of the equatio x-x+-7=0, the the value of cos A cos B cos C is equal to a b c Q Q 7 7 The straight roads itersect at a agle of 0 A bus o oe road is km away from the itersectio ad a car o the other road is km away from the itersectio the the direct distace betwee the two vehicles is km km km 7 km If i a triagle ABC cos A cos B cos C a b a b c bc ca the the value of the agle A is Q0 If i a triagle ABC, bc ca ab the cos A is equal to 7 oe of these

7 si cos for some 0 The the greatest Q The sides of a triagle are sia, cosa ad Q agle of the triagle is If the area of a ABC be the a si B+b si A is equal to Q a) b) c) d) oe of these I a ABC, A:B:C=:: The a b c is equal to a) c) Q b b I a ABC, A= b) d) c a, b-c= cm ad ar ( ABC)= cm The a is a) cm b) cm c) cm d) oe of these 7

8 Class - XI Maths Assigmet 0-07 Topic : Sequeces ad Series Sectio-A Q Show that the sequece <a> defied by a = + is ot a AP Q Fid the umber of idetical terms to the two APs,, upto 0 terms ad,, 7,, upto 0 terms (0) Q Fid the sum of first terms of the AP a,, a if it is kow that a+a+a0+a+a0+a= (00) Q If s, s, sm are the sum of terms of m APs whose first terms are,, o ad commo differeces are,,, (m ) respectively Show that s s s m m m A eve o of AM's are beig iserted betwee them ad their sum exceeds their umber by Fid the o of meas iserte () Q The sum of two umbers is Q If a, b, c, d, e, f, are i AP the prove that e c=(d c) ad a b+c d+e=0 Q7 I a AP, t7=, the fid the value of commo differece d that would make t t7t greatest (0) Q The sum of three terms of a AP is ad their product is 7 Fid the least term Q The sum of the first four terms of a AP is The sum of the last terms is If the first terms is, fid the o of terms () Q0 The umbers t(t +), ½t ad are cosecutive terms of a AP If t be real, the fid the ext two terms of the AP (, ) Q If Q If the sum of first terms of the AP,,, is equal to the sum of the first terms of the AP 7,,, the fid () Q Fid the sum of terms of a AP whose middle term is 0 Q Fid the umber of umbers lyig betwee 00 & 00 which are divisible by 7 but ot by Q Fid the coefficiet x i (x+)(x+)(x+)(x+) Q If a, a, a are i AP, where ai>0, i, the evaluate 7 7, fid 0 terms i a a a a ii a a a a a a a a () () () (0) N a a a a ( )(a a ) a a a a a a (0) k a a k if <a> is a AP k Q7 PT a a a a a k Q There are AM's betwee & such that th mea : (-)th mea= : Fid () Q Evaluate a+b+c+d+e+f if a, b, c, d, e f are AM's betwee & () Q0 PT a, b, c are i AP iff,, are i AP bc ca ab

9 Q Fid the coefficiets of x, x, x7 i (x+)(x+)(x+)(x+)(x+) Q Fid the sum to terms Q If S is the sum of AM's betwee a & b ad A is the sigle arithmetic mea betwee a & b, the evaluate S/A () + + upto terms 7 7 Q If a, a, a are i AP, ST a a a a a a a a Q I a sequece, the first o is (,0, 077) ( ) ( )( ) The d o is first o divided by more tha the first o The rd o=d o divided by more tha the d o ad so o What is the 00th term of the sequece? 0 Q If the fifth term of a GP is Fid the product of its terms Q7 If ap+q=m ad ap q=, fid ap if these are terms of a GP m Q If a=+b+b+b+ Write b i terms of a a Q Fid the sum to ifiity x x x x ( x ) x x Q0 If x=(00), fid x Q If Q Fid all sequeces which are simultaeously AP ad GP Q I a icreasig GP, the sum of the first ad last term is, the product of the secod ad the last but oe term is If the sum of the series is, fid the umber of terms i the series () Q r r r () r, fid r ad r (0, ) (Costat) If S is the sum of terms of a GP {a} ad S is the sum of terms of the sequece, the a show that S=aas' Q Let x be the arithmetic mea ad y, z be two geometric meas betwee ay two positive umbers, prove that y+z=xyz Q If x, y, z are distict positive umbers, prove that (x+y)(y+z)(z+x)>xyz Further if x+y+z=, show that ( x)( y)( z)>xyz Q7 A Sail starts movig towards a poit cm away at a pace of cm per hour As it gets tired, it covers oly half the distace compared to previous hour i each succeedig hour I how much time will the sail reach its target? (Never reach) Q I a set of four umbers, the first three are i GP ad the last three are i AP with a commo differece of If the first umber is same as the fourth, fid the four umbers (,,, ) Q If x>0, prove that x x

10 Q0,, are i AP c d e (,, ), (,, ) Let a, b, c, d, e be five real os Such that a, b, c, are i AP b, c, d are i GP If a= ad e=, fid all possible values of b, c, ( )( ) Q Fid the sum of the series +( )+( )++ Q Fid the sum to terms Q Fid the sum of product of first atural os take two by two Q Q Q Q Q Q Q7 If +x + x, a ad x+ x are three cosecutive terms of a AP, the the values of a are give by a a> a< a If the series of atural umbers is divided ito groups (); (,,); (,,7,,), ad so o, the the sum of the umbers i the th group is +(+) +(+) ( ) + ( ) + If x, y, z are i AP where the distict umbers x, y, z are i GP, the the commo ratio of GP is / / If the sum of four umbers i GP is 0 ad the AM of the first ad the last is, the the umbers are,,,0,,,,,, oe of these Sum to ifiity of the series is oe of these 0 upo terms : () + () is equal to digits Q0 Q ( )( )( ) Sectio B (Objective Type Questios) The umber of umbers lyig betwee 00 ad 00 that are divisible by 7 but ot by is 7 oe of these The largest term commo to the sequeces,,,, to 00 terms ad,,,, to 00 terms is 7 oe of these Q ( ) ( )( ) upto terms digits 0 If the sum of the series 0 oe of these 7 upto terms 0

11 Q I a sequece of (+) terms the first (+) terms are i AP whose commo differece is, ad the last (+) terms are i GP whose commo ratio is 0 if the middle terms of the AP ad GP are equal the the middle term of the sequece is Q Q oe of these The coefficiet of x i the polyomial (x )(x )(x )(x ) is oe of these If (-p)(+x+x +7x+x+x)=-p, p the the value of p is x If the sides of a right agled triagle are i AP the the sies of acute agles are Q Q Q Q7,,, oe of these Value of is equal to oe of these oe of these The value of 0 is Q I a GP the first, third ad fifth terms may be cosidered as the first, fourth ad sixteeth terms of a AP The the fourth term of the AP, kowig that its first term is is Cosider the te umbers ar, ar, ar, ar If their sum is ad the sum of their reciprocals is the the product of these te umbers is Q Suppose a, b, c are i AP ad a, b, c are i GP If a>b>c ad a+b+c=, the the value of a is Q0 If a i, where a, a, a, a are i AP, the the value of Q The cosecutive odd itegers whose sum is are,, 7,, 7,, i 0 a r r 0 is,,

12 Class - XI Maths Assigmet 0-07 Topic : Complex Numbers, Quadratic Equatios & Liear Iequatios x i a ib, prove that a b x x Q If Q Fid the value of z +z+7z z+ if z i Q Evaluate 0 Q If z, & z be ay complex umbers, the show that i Re(z z )=Re(z )re(z ) Im(z )Im(z ) ii Im(Z,z )=Re(z )Im(z )+Im(z )Re(z ) Q Fid real such that Q x 0 i si is i si =, z purely real ( ) si, purely imagiary If a b ci, ab,c R, show that c i a+b= ad b c a c Q7 If a & b are differet complex umbers with, the fid the value of Q If (+i)(+i)(+i)=x+iy,st 0(+ )=x+y Q Let z=x+iy ad w Q0 For ay two complex umbers z & z, Prove that z z z z Q Q iz If w =, the show that z is purely real z i z z Fid the modules ad pricipal argumet of i i i, ii i cos i si, If z & z be two o-zero complex umbers such that z z z z, fid arg(z) arg(z) Q x y x y Fid the square root of i y x y x Fid z if iz+z z+i=0 Q If z = z == z =, prove that z z z Q x y i y x z z z

13 Q If z <, prove that iz Q7 If Q Q Q0 a ib, prove that a+b=a cos i si Express (+x)(+y)(+z) as the sum of two squares (xy x y z) (xy+yz+zx ) Show that (x +y )=(x x y+y ) +(x y xy ) Show that the area of the triagle o the Argad plae formed by the complex umbers z, iz ad z Solve the followig equatios over C z+iz is Q Q x i x i 0 ii x ( i)x+(+i)=0 iii x x +x x +x =0 Solve i i, i, +i iv x x7 ii x+y =, x y= x, x 7 x7 x x x iv,, x 7x x 7 x A electricia ca be paid uder schemes as give below : I: Rs 00 ad Rs 70 per hour II : Rs0 per hour If the job take x hours, for what values of x does the scheme II give the electricia better ways : A maufacturer has 00 litres of a % solutio of aci How may litres of a 0% acid solutio must be added to it so that acid cotet i the resultig mixture will be more tha % but less tha %? 0 l < x < 00 l Solve graphically : i x+y ii x+y 7x+y x+y x, y x+y x, y 0 x, y x, y iii Q Q Q Q i ii x x x x (, ) (, ) x How may litres of water will have to be added to litres of the % solutio of acid so that the resultig mixture will cotai more tha % but less tha 0% acid cotet! iii Q7 x 7x 7x x, x x Q Solve x x x Q Solve x, x Q0 Solve x iv,0, 7,,,, 0, x R, x i x ii ; x R, x x,,

14 Class - XI Maths Assigmet 0-07 Permutatios & Combiatios Q Fid if Cr : Cr+ : Cr+ = : : Q How may arragemets ca be made usig the letters of the word MATHEMATICS? I How (=)!!!!!!!!! may of them are the vowels together? Q A committee of is to be formed from me ad wome I how may ways ca this be doe if at least wome are iclude at most wome are iclude c b c c bc c c c b c c bc b c Q Fid the rak of the word FARIDABAD as writte i the dictioary (00) Q Fid the umber of proper divisors of 0 Q The result of football matches (wi, loss, draw) are to be predicte How may differet forecast ca cotai exactly correct results C Q7 For a set of six true or false questios, o studet has writte all the correct aswers ad o studet have give the same sequece of aswers What is the maximum umber of studets i the class, for this to be possible () Q I how may ways ca this diagram be coloured subject to the followig coditios? () i Each of the smaller triagle to be paited with oe of the colours : red, blue or yellow () ii No two adjacet regios receive the same colour () Q How may atural os ot exceedig ca be formed with the digits,, ad, if the digits ca repeat? () Q0 Fid the umber of zeros at the ed of 0! Q If all the permutatios of the letters of the word INDIA are arraged as i a dictioary, what are the th, th, 0th ad 0th words (DAINI, NADIIM, NAIDI, NIIDA) Q I how may ways ca getleme & ladies be seated at a roud table so that o two getleme are together? (0) Q If & r are positive itegers r, show that () C r+ C r + C r = +C r Q A studet has library tickets ad books of his iterest i the library Of these, he does ot wat to borrow chemistry part II, uless chemistry part I is also borrowe I haw may ways ca be choose the books to be borrowed? ( C + 7C ) Q A ma has childre to take them to a zoo He takes three of them at a time to the zoo as ofte as he ca without takig the same childre together more tha oce How may times will he have to go to the zoo? How may times a particular child will go to the zoo? ( C + 7C )

15 Q There are 0 poits i a plae Of these 0 pts, pts are i a straight lie ad with the exceptio of these pts, o three pts are i the same straight lie Fid (i) the o of triagles forme (ii) The o of straight lie formed (iii) the o of quadrilaterals formed, by joiig these te poits (i) 0 C C (ii) 0 C C+ (iii) 0 C C C C Q7 Six X s have to be placed i the square of the figure give, such that each row cotais at least oe x, i how may differet ways ca this be doe? (C ) Q I a group of boys, there are hockey players I how may ways ca boys be selected so as to iclude at least hockey players? ( C C + C C 7+ C C ) Q How may words with or without meaig each of vowels ad cosoats ca be formed from the letters of the word DAUGHTER? (C C!) Q0 How may -letter words ca be made usig the letters of the word ORIENTAL? Q I the figure, two -digit umbers are to be formed by fillig the places with digits The umber of differet ways i which the places ca be filled by digits so that the sum of the umbers formed is also a -digit umber ad i o place the additio is with carryig, is (d) Q Q 0 oe of these Th H The umber of proper divisors of pqr is (p) T U (b) (p+q+)(q+r+)(r+) (p+q+)(q+r+)(r+)- (p+q)(q+r)r- oe of these The umber of proper divisors of 00 which are also divisible by 0, is 7 oe of these (d) Subjective questios : Q I how may ways ca people be seated i a car with two people i the frot seat ad three i the ( p p ) rear, if two particular persos out of the five caot drive? Q How may o-zero umbers ca be formed usig the digits 0,,,, ad if repetitio of digits is ot allowed? (0) Q What is the largest iteger such that 0 is divisible by? Q7 Prove that (i) Pr=r Pr + Pr (ii) +P+P+P++P=+P+ Q How may eve umbers are there with three digits such that if is oe of the digits i a umber the (7) 7 is the ext digit i that umber () Q How may umber of -digits ca be formed with the digit,, ad Fid the sum of those umbers Q0 How may differet words ca be formed with the letters of the word UNIVERSITY so that (i) all the vowels are together (ii) all vowels are ot together (iii) o two vowels are together (iv) all vowels are together ad the cosoats are together (i) 7!! 7!!7 p! (ii) 0!! (iii) (iv)!!!!!

16 Q Q I how may ways ca the letters of the word ARRANGE be arraged so that i the two R s are ever together? (00) ii the two A's are together but ot the two R's? (0) iii either the two A's or the two R's are together? (0) If Cr : Cr : +Cr= : :, fid ad r 7 C r i C (C) Q Fid the value of the expressio Q Q Fid the umber of divisor of 00 Fid the total umber of ways of selectig -letters from the letters of the word INDEPENDENT (70, 00) The letters of the word OUGHT are writte i all possible orders ad these words are writte out as i a dictioary Fid the rak of the word TOUGH i the dictioary Fid the rak of the word ROBIN whe all letters are arraged to form a dictioary Fid the umber of (i) permutatios (ii) selectio of -letter words formed with the letters of the word PROPORTION Fid the rak of the followig words whe the letters are arraged as i a dictioary (i) INDIA (ii) RUSSIA (iii) MOTHER (iv) SHOBIT Fid the umber of (i) permutatios (ii) selectios of - letter words formed with the letters of the word (a) MATHEMATICS (ii) PROPORTION (iii) MISSISSIPPI There are 7 boys ad girls I how may ways ca they be seated i a row so that (i) o restrictio (ii) all girls sit together (iii) all girls do ot sit together (iv) o two girls sit together Fid the umber of sides of a polygo havig 0 diagoals We wish to select persos from persos, but if the perso A is chose, the B must be chose I how may ways ca the selectio be made? There are 0 poits i a plae of which are colliear No three of the remaiig poits are colliear How may differet (i) straight lies (ii) triagles formed by joiig these poits Q Q7 Q Q Q0 Q Q Q Q i

17 Class - XI Maths Assigmet 0-07 Biomial Theorem Q Fid the coefficiet of x i the expasio of x x Q Fid the middle term i the expasio of (x +y) x Fid the term idepedet of x i the expasio of x Q Show that Q Q Q (7) 0 0 C is a eve positive iteger ad hece fid the itegral value of (7) The coefficiets of cosecutive terms i the expasio of (+x) are i the ratio : : Fid (7) If P be the sum of the odd terms ad Q that of the eve terms i the expasio of (x+a) prove that i (x a ) =P Q ii (x+a) (x a) =PQ iii (x+a) +(x a) =(P +Q ) Prove that i (+x)-x- is divisible by x N ii -- is divisible by Q7 Q Q I the expasio of, the ratio of 7th term from the begiig to the 7th term from the ed is :, fid () r- r r+ If the coefficiets of x, x ad x i the biomial expasio of (+x) are i AP, prove that -(r+)+r -=0 () If a, a, a, a be the coefficiets of four cosecutive terms i the expasio of (+x), the prove that a a a a a a a a a Q0 Q Fid the umber of itegral terms i the expasio of ( /+7/)0 If a, b, c ad d i ay biomial expasio be the th, 7th, th ad th terms respectively, the prove that b ac a c bd c i the expasio of x x x Q Fid the coefficiet of Q Q Fid the coefficiet of x i the expasio of (+x) +(+x)++(+x) 0 Write the umber of terms i the expasio of i Q x 0 x 0 ( C ) ( C C ) () ii ( x+x x ) () 0 iii (x+y+z) C If a & b deote the sum of the coefficiets i the expasios of ( x+0x ) ad (+x ) respectively, the write the relatio betwee a ad (a=b) 7

18 Q Fid a, x ad i the expasio of (a+b) if the th, 7th ad th terms i the expasio of (x+a) are, 7 ad respectively (=,x=,a=½) Q7 Prove that the coefficiet x i (+x) is twice the coefficiet of x i (+x) Q x x Fid the coefficiet of the term idepedet of x i the expasio of (0) x x x x 0 Q Q0 Q ad x 7 i ax ad fid the relatio betwee a & Fid the coefficiet of x i ax bx bx b so that these coefficiets are equal (ab=) Usig biomial theorem Prove that (0) >00 + Usig biomial theorem, idicate which is larger () 0000 or 000 () Q Fid the sum of ratioal terms i the biomial expasio of () m Q Q Q The sum of the coefficiets of the first three terms of the expasio x, x 0, m beig a x atural umber, is Fid the coefficiet of x ( C()) For what values of m the coefficiet of the (m+) th ad (m+)th terms i the expasio of (+x) 0 are equal (m=) Show that the middle term i the expasio of (+x) is ( ) x!

3sin A 1 2sin B. 3π x is a solution. 1. If A and B are acute positive angles satisfying the equation 3sin A 2sin B 1 and 3sin 2A 2sin 2B 0, then A 2B

3sin A 1 2sin B. 3π x is a solution. 1. If A and B are acute positive angles satisfying the equation 3sin A 2sin B 1 and 3sin 2A 2sin 2B 0, then A 2B 1. If A ad B are acute positive agles satisfyig the equatio 3si A si B 1 ad 3si A si B 0, the A B (a) (b) (c) (d) 6. 3 si A + si B = 1 3si A 1 si B 3 si A = cosb Also 3 si A si B = 0 si B = 3 si A Now,