CBSE|CLASS X|MATHS WORKSHEET|TRIGONOMETRY

[Pages:2]CBSE|CLASS X|MATHS WORKSHEET|TRIGONOMETRY

WWW. INTRODUCTION TO TRIGONOMETRY

1) If sin cos , find the value of ' ' .

2) If sin A = 3 , calculate cos A 5

3) Evaluate: cos 480cos 420 - sin 480 sin 420

4) If A, B and C are the interior angles of a triangle ABC, then show that tan B C cot A . 2 2

5) Prove that 1 cos A cosecA cot A . 1 cos A

6) If cosec 13 , evaluate 2sin 3cos .

12

4sin 9cos

7) In a right angled ABC, B = 900.If BC = 1 , then find AB

AB 3

AC

8) Express the trigonometric ratioscos A, tan A and sec A in terms of sin A

9) In ABC, right-angled at C find cos A, tan A and cosec B if sin A = 24 25

10)

In triangle ABC, right-angled at B, if tan A =

1 3

,

find

the

value

of:

(i) sin A cos C + cos A sin C (ii) cos A cos C ? sin A sin C

11) Prove that sec A (1 ? sin A)(sec A + tan A) = 1.

12) If A, B and C are interior angles of a triangle ABC, then show that s + =

2

2

13) Evaluate: tan 2 60 4cos2 45 3sec2 30 5cos2 90 cosec30 sec60 cot2 30

14) Prove that cos A sin A 1 cosecA cot A using the identity cosec2 A 1 cot2 A . cos A sin A 1

15) Write all the other trigonometric ratios of A in terms of sec A.

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CBSE|CLASS X|MATHS WORKSHEET|TRIGONOMETRY

WWW. 16) Prove the following identity, where the angles involved are acute angles for which the

expression is defined:

1 sin A

= sec A + tan A

1 sin A

17) In an acute angled triangle ABC if sin(A + B ? C) = 1 and cos( B + C ? A)= 1 find

2

2

A , B and C

18)

Prove that :

1+ 2 1+ 2

=

1-

2

=

1-

2

19) Evaluate :

(i)

2 630 + 2 270 2 170 + 2 730

(ii) sin 25o cos65o + cos25o sin65o

20) In OPQ, right-angled at P, OP = 7 cm and OQ ? PQ = 1 cm. Determine the values of sin Q and cos Q.

21) If B and Q are acute angles such that sin B = sin Q, then prove that B = Q.

22) If sin (A ? B) = 1 , cos (A + B) = 1 , 0? B, find Aand B.

2

2

23) If sin 3A = cos (A ? 26?), where 3A is an acute angle, find the value of A.

24) Prove that sin A cos A 1

1

, using the identity sec2 1 tan2 .

sin A cos A 1 sec A tan A

25) Prove that (cosecA sin A)(secA cos A)

1

.

tan A cot A

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