. o o o o {cos 4 cos 9 si cos 65 } si 7º () cos 6º si 8º. If x R oe of these, the mximum vlue of the expressio si x si x.cos x c cos x ( c) is : () c c c c c c. If ( cos )cos cos ; 0, the vlue of 4. The vlue of t / t / Ojective Mthemtics Er.L.K.Shrm () 4 6.cos.cos.cos.cos 5 5 5 5 () 5. If cos si c d cos si c, the 6. If t, t re the roots of qudrtic equtio x px q 0, the vlue of expressio si ( ) qcos ( ) psi( ).cos( ) p q q p q () p q q p 7. If t, the cos(8 ) p p p + p () p p oe of these 8. The vlue of {si 44º. si 08º. si7º. si6º} is equl to : 6 9. The vlue of () 5 6 7 6 6 6 4 t 0 t 0 7 t 0 is : () 4 0. The vlue of oe of these 7 9 cos cos cos cos 0 0 0 0 8 () 6 oe of these vlue of t. If cos A si A, m, the si B cos B si B () c m () m c m m [ 00 ] Mthemtics for JEE-0 Author - Er. L.K.Shrm
Trigoometric Rtios d Idetities. If / / f ( ) ( cos si ) ( si cos ) the mximum vlue of f ( ) is : () ( ) 4 9. If f ( ) si si si ; the vlue of f 5 oe of these () t x. Let f ( x) d x or ; I, the t x itevl i which f (x) lies is : R, R, () R, R, 6 6 4. If cos si K si ( ) ; 0, the vlue of K 4 () 4 8 o o o o 5. The vlue of cos 0 cos0.cos 50 cos 50 is : 4 4 () Ojective Mthemtics Er.L.K.Shrm 6. If A + B + C = 0, the vlue of the expressio {si A+cos C(cos A cos B cos C)+ cos B (cosa cosc cosb)} () 0 0. If cot A, cot B, cot C re i A.P. for ABC, the si A cos B si C is : t B sec B. Let, i i R si () si B cot B i,,. if for ll si i cos i i i si i.cosi i d si i cos i i i cos, the si i.cos i i. Let 4 4 si cos. () si cos. 4 8 8 8 si cos. si cos. cos A cos B cos B d si A si B si B, the si ( B ) is : 5 4 () 8 9 6 7. Vlue of (t 40º + tº 0) is : cot 50º () cot 40º cot 0º cot 0º. Let for ll / x x x R, t, x x where 8. 8 o si (5 r) r 9 () 9 7 (0, ),, the vlue of ' ' c e : 8 6 5 () 5 [ 0 ] Mthemtics for JEE-0 Author - Er. L.K.Shrm
si x/ cos x/ 4. The miimum vlue of (8) (7) equl to : sec () t 8 si is cosec = = 5 = 0 () 0 + + 4 + 6 = 0 6 + 0 = 0 0. Vlue of equl to : 6 r r 0 0 55 o o ( t( r )). ( cot( r )) is r r 46 5. Let, R d, the mximum vlue of {si si } () 04 0 () 0 0 r0 0 r0 0 C C r r 6. Let r f ( ) t. ( sec( )), the r f 6 () f 64 f 48 f5 8 7. Which of the followig re rtiol umers? si.cos si.cos 0 5 Ojective Mthemtics Er.L.K.Shrm ().cosec sec 9 9 si º. si 48º. si 54º 8. Solutio set {x, y} for the system of equtios 9. If x y = d cos ( x) si ( y) c e give y : 7 5, 6 6 5 7, 6 6 6 m0 (),, 6 6 m si x.si x m cos x, where 0,,,... 6 re costts, the Followig questios re ssertio d resoig type questios. Ech of these questios cotis two sttemets, Sttemet (Assertio) d Sttemet (Reso). Ech of these questios hs four ltertive swers, oly oe of them is the correct swer. Select the correct swer from the give optios : Both Sttemet d Sttemet re true d Sttemet is the correct expltio of Sttemet. () Both Sttemet d Sttemet re true ut Sttemet is ot the correct expltio of Sttemet. Sttemet is true ut Sttemet is flse. Sttemet is flse ut Sttemet is true.. I trigle ABC with fixed se BC, t he A vertex A moves such tht cos B cosc 4si. If, d c deote the side legths of trigle opposite to the gles A, B d C respectively, the. Let Sttemet : locus of vertex poit A is ellipse ecuse Sttemet : I the give ABC,, d c form rithmetic progressio. 4 4 si cos, where R, the 7 0 8 8 si cos Sttemet : Vlue of is equl to 7 4 sgl. log 0 0 ecuse Sttemet : Vlue of t. 7 [ 0 ] Mthemtics for JEE-0 Author - Er. L.K.Shrm
Trigoometric Rtios d Idetities. Let,, R, d cos, cos c c d cos, where the sides,, c of trigle ABC re i A.P. Sttemet : Vlue of t to ecuse t is equl Sttemet : p t d t p 4. Sttemet : For t rigle ABC, if si A si B si C, the trigle must e right gled ecuse Sttemet : I y trigle PQR, si P si Q si R ( 4 cos P.cos Q.cos R) 5. Cosider y trigle ABC hvig iterl gles, d, where,,. Sttemet : If Ojective Mthemtics Er.L.K.Shrm t t t 6 4x x for ll x R, the trigle ABC is essetilly cute gled trigle ecuse Sttemet : I y trigle except the right-gled, sum of the tget of iterl gles is lwys equl to the product of tget of iterl gles. [ 0 ] Mthemtics for JEE-0 Author - Er. L.K.Shrm
Comprehesio pssge () ( Questios No. - ) Let ; where I, d cos si....() cos( ) si( ) O the sis of give reltio, swer the followig questios.. Usig the idetity 4 4 cos si cos, the vlue of t which is otied from the give reltio... () of pssge cos si cos si () cos si si cos. Usig the idetity si.cos cos si si cos, the vlue of t which is otied from the give reltio...() of pssge cos si x si cos () si cos x Ojective Mthemtics Er.L.K.Shrm si cos. If ' ' is elimited from reltio...() of pssge, the qudrtic i which is otied, cos 0 () si 0 cos 0 si 0 Comprehesio pssge () ( Questios No. 4-6 ) 9 Let vlue of t, where 4 > > 0, the swer the followig questios. 5. The vlue of () 4 4 cos(r ) r0 8 () o o o o 6. The vlue of t 6.t 4.t 66.t 78 is 7. If equl to : T si 4 6 T T 8. If si 4 9. If x cos () x, is equl to... t he vlue of is root of the cuic equtio 8x 4x 4x 0 d [.] represets the gretest iteger fuctio, the vlue of is equl to... 4 7 (r ) si, 4 the vlue of r is equl to... 4. The vlue of equl to : 4 8 4 cos.cos.cos.cos 5 5 5 5 is 0. Let 8, d e three sides of trigle, the lest possile itegrl vlue of ' ' is equl to... [ 04 ] Mthemtics for JEE-0 Author - Er. L.K.Shrm
Trigoometric Rtios d Idetities. Let si si d cos cos, where, the mtch the followig colums (I) d (II). Colum (I) Colum (II) t t (p) ( ) 4 4( ) () cos.cos (q) ( ) cos 8 (r) ( ) 4 4 si( ) (s) ( ) (t). Mtch the followig colums (I) d (II). Colum (I) Ojective Mthemtics Er.L.K.Shrm Colum (II) If x,, the the output set of (p) (, ] si x si x f ( x) 4 4 coti the itervl(s) () If x, 0, the the output set of (q) [4, 5) 6 4 f ( x) si x si x 5si x cos x (r) (5, 9] coti the itervl(s) If x,, the the output set of (s) [, 4) f (x) = t 6 x + 4 t x + 5 coti the itervl(s) If x,, the output set of (t) [, 4) sec x sec x f ( x) 9 4() 5 coti the itervl(s) [ 05 ] Mthemtics for JEE-0 Author - Er. L.K.Shrm
.. (). 4. 5. Ex 6. 7. 8. () 9. 0. (). (). (). () 4. 5. 6. 7. () 8. () 9. () 0. ().. (). 4. 5. 6. (,, c) 7. (,, c, d) 8. (, c d) 9. (,, c) 0. (, ).. (). 4. 5.. ().. 4. () 5. Ex 6. 7. ( 6 ) 8. ( 0 ) 9. ( 9 ) 0. ( 6 ). r. s () p () q, r, s t p, q, r, s, t q q Ojective Mthemtics Er.L.K.Shrm [ 06 ] Mthemtics for JEE-0 Author - Er. L.K.Shrm