X Maths: Chapter 8 Trigonometry

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1 X Maths: Chapter 8 Trignmetry EXERCISE Given 5 ct = 8, find If 8 = 5, find cs In figure find P ct R 4 In a right triangle BC, right-angled at B, if =, then verify that cs = 5 In OPQ, right-angled at P, OP = 7 cm and OQ PQ = cm Determine the values f Q and cs Q 6 In PQR, right-angled at Q, PR + QR = 5 cm and PQ = 5 cm Determine the values f P, cs P and P 7 In triangle BC, right-angled at B, if =, find the value f: (i) cs C + cs C (ii) cs cs C C 8 In BC, right angled at C, if = 7 ( )( ) 9 If ct =, evaluate 8 ( cs)( cs) If ct = 4, check whether a a b cs If =, then is equal t b a b cs, and B =, prve that ( cs B + cs B) = = cs r nt If = a b, find the values f ther five trignmetric ratis a b If cs - 4 = cs +, find 4 If, find the value f 5 If mn, find the values f ther t-ratis f ( m n ) 6 If 7 = 4 cs, prve that cs 7 sec = 7 In the figure, CD B If D = 4 units, DB = 6 units and CD = units, find the values f (i) (ii) ct (iii) sec B (iv) B

2 8 In the figure BC is a right angled at B BSC is right angle at S, and BRS is right angled at R, B = 8 cm, BC = 75 cm, RS = 5 cm and SB = y Find (i) x (ii) y (iii) cs y BSR = x 9 In the figure B = 9 a, BC = CD =, BC = and D = b Find (i) (ii) cs Ug the measurement given in the adjining figure, find (i) cs (ii) (iii) csec Test Yurself BC has a right angle at BC =, B = C = Write dwn B, cs C and B 4 if csec =, Find the values f and sec 4 ct If cs =, evaluate 5 4 If 4 = cs, find the value f 7cs 8 cs 5 If =, shw that 4 Exercise In BC, right-angled at B, B = 5 cm and CB = Determine the sides BC and C In PQR, right-angled at Q, PQ = cm and PR = 6 cm Determine QPR and PRQ Evaluate the fllwing : (i) 6 cs + cs 6 (ii) 45 + cs 6 (iii) cs 45 sec csec (iv) 6 sec 45 cs 45 6

3 (v) 5 cs 45 4 cs 45 4 Chse the crrect ptin and justify yur chice : (i) () 6 (B) cs 6 (C) 6 (D) (ii) () 9 (B) (C) 45 (D) (iii) = is true when = () (B) (C) 45 (D) 6 (iv) = () cs 6 (B) 6 (C) 6 (D) (v) The value f 6 6 is equal t () (B) cs (C) ct (D) 5 If = then is equal t () (B) cs (C) (D) 6 If = then 4Cs cs is () (B) (C) cs (D) cs 7 If ( + B) = and ( B) = ; find and B 8 If ( B) =, cs ( + B) =, find and B Taking =, verify each f the fllwing : (i) = cs (ii) cs = 4cs - cs Taking = 6 and B =, verify that ( B) = cs B cs B 4 If = B = 45, verify that, (i) ( + B) = cs B + cs B (ii) ( B) = B B

4 6 Find the value f x in each f the fllwing : (i) x = (ii) x = cs x (iii) x = 45 cs45 + (iv) csx = cs6 cs + 6 (v) Cs ( 4 + x ) =, find x Exercise Evaluate (i) 8 cs7 (ii) csec sec 59 ct (9 - ) sec (9 - ) csec sec5 ct 4 csec 4 cs 4 csec5 4 cs cs cs sec ct cs ( 9 cs5 75 ) cs(9 ) 6 7 ct (9 ) (9 ) ct 4 - (cs + cs 7 ) 5 ct csec7 sec7 8 Shw that = 9 Shw That cs 8 cs = Shw that: = Shw that: cs cs cs cs 99 cs = Shw that: 6 9 = Prve that (i) (5 + ) cs (4 - ) = (ii) cses (65 + ) sec (5 - ) = If 5 = cs 4, where 5 and 4 are acute angles, find the value f If sec 5 = csec ( - 6 ), where 5 is an acute angle, find the value f 4 If,B,C are the interir angles f a triangle BC, prve that 4

5 (i) C B ct B (ii) cs 5 Find the degree measure f satisfying ( + 45 ) = cs ( - ) 6 If = cs ( 6 ), where is an acute angle, find the value f 7 If = ct ( 8 ), where is an acute angle, find the value f 8 If = ct B, prve that + B = 9 9 Express 67 + cs 75 in terms f trignmetric ratis f angles between and 45 Express cs in terms f in terms f sec in terms Evaluate Exercise 4 4 cs 7 6 cs cs 65 + cs sec 9 7 ( + + sec ) ( + ct csec ) Prve that 8 cs - = 9 sec = (sec ) (csec ) = ( + ) cs = ( + )( )( + ) = (sec + ) ( ) = cs 4 ct = 5 sec ( ) (sec + ) = ct cs 6 = ct cs csec csec 7 cs = cs sec 8 cs = csec + ct, cs 9 (csec - ct ) = cs cs cs sec cs 5

6 sec sec cs = sec + cs cs 4 ( + csec ) + (cs + sec ) = ct 5 (csec ) (sec cs ) = ct ct ct 6 - = - sec - cs cs sec + sec 4 sec = 4 + If + =, prve that cs + cs 4 = 4 Prve that (i) ( cs B cs B) = ( B) (ii) ( sec B sec B) = ( B) csec cs csec sec sec sec x x sec = csec sec cs x cs x sec x x cs ec ct cs ec ct If x = a cs and y = b, prve that b x + a y = a b If m - n cs = p and m cs + n = q, then prve that m + n = p + q 4 + cs 4 = cs 6 + cs 6 = cs Bard Questins (CBSE 6) Prve that cs cs sec cs cs 6

7 Evaluate withut ug Trignmetric Tables sec (9 ) ct cs ( 5 65 ) (sec 4 ct 47 ) The angles f depres f the tp and the bttm f a building 5 meters high as bserved frm the tp f a twer are and 6 respectively Find the height f the twer and als the hrizntal disce between the building and the twer The angle f elevatin f the tp f a twer as bserved frm a pint n the grund is and n mving p meters twards the twer, the angle f elevatin is Prve that the height f the twer is p (CBSE 7) 4 by sding n a hrizntal plane finds a bird flying at a disce f m frm him at an elevatin f girl sding n the rf f meter high building, find the angle f elevatin f the same bird t be 45 Bth the by and the girl are n ppsite sides f the bird Find the disce f bird frm the girl 5 If = 5, find the value f ( + cs ) sec 6 If sec 4 = csec ( ), where 4 is an acute angle, find the value f In a BC, right angled at C, if =, find the value f cs B + cs B (CBSE 8) 7 Prve that (+ ct + ) ( cs ) = ct cs evaluate cs58 cs8 csec cs 8 Prve that cs ct Evaluate cs55 4 (cs7 csec (CBSE 9) 9 If =, then find the value f ( ct + ) cs Simplify : cs cs evaluate cs58 cs68 cs8 csec

MOCK CBSE BOARD EXAM MATHEMATICS. CLASS X (Paper 1) (AS PER THE GUIDELINES OF CBSE)

MOCK CBSE BOARD EXAM MATHEMATICS. CLASS X (Paper 1) (AS PER THE GUIDELINES OF CBSE) MOCK CSE ORD EXM MTHEMTICS CLSS X (Paper 1) (S PER THE GUIDELINES OF CSE) Time: 3 Hurs Max. Marks: 80 General Instructins 1. ll the questins are cmpulsry. 2. The questin paper cnsists f 30 questins divided