TRIGONOMETRY
CLASS: X : MATHEMATICS
1. Simplify: cos4 A – sin4A
2. If ∆ABC is right angled at C, then find the value of cos(A + B).
3. If sin A+ cosA = √2 cosA, then find the value of tan A.
5sin 3cos
4. If 5 tan θ = 4, then find the value of
5sin 2 cos
4sin cos
5. If 4 tan θ = 3, then find the value of
4sin cos
2 sin A 3cos A
6. If cosec A = 13/12, then find the value of
4sin A 9 cos A
7. In ΔABC, right angled at B, AB = 5 cm and sin C = 1/2. Determine the length of
side AC.
8. In ∆ABC, right-angled at C, if tan A=1, then find the value of 2sin A cos A.
1
9. If for some angle θ, cot 2θ = , then find the value of sin3θ, where 3θ ≤ 90⁰.
3
10. If tan θ = 1, then find the value of sec θ + cosec θ.
11. If is an acute angle and tan + cot = 2, then find the value of sin3 + cos3 .
7
12. In ABC right angled at B, sin A = , then find the value of cos C.
25
13. Find the value of (sin 45° + cos 45°).
m
14. Given that sin θ = then find cos θ.
n
4
15. If cos A = , then find the value of tan A.
5
16. In ΔABC right angled at B, if tanA = √3, then find the value of
cosA cosC – sinAsinC.
17. If 2sin2 β – cos2 β = 2, then find β.
18. If √3 tan θ = 1, then find the value of sin2 θ – cos2 θ.
19. In a right triangle ABC, right-angled at B, if tan A = 1, verify that 2 sin A cos A = 1.
1
20. If sin 2A = tan² 45° where A is an acute angle, then find the value of A.
2
21. If sec A = 15/7 and A + B = 90°, find the value of cosec B.
22. Find A and B, if sin (A + 2B) = √3/2 and cos (A + B) = 1/2.
23. If (1 + cos A) (1 – cos A) = 3/4 , find the value of tan A.
24. Evaluate: 3 cos2 60° sec2 30° – 2 sin2 30° tan2 60°.
KRISHNA'S INSTITUTE : 2nd Floor, Jaipuria Plaza, Sec - 26, Noida (U.P) Page - 1-
cos sin 1 3
25. Find an acute angle θ when
cos sin 1 3
(1 sin )(1 sin )
26. If tan θ =3/4, evaluate
(1 cos )(1 cos )
1 1
27. If sin(A – B)= , cos(A + B) = , 00< A + B ≤900 , A > B. Find A and B.
2 2
28. If sin(A + B) = 1 and cos(A – B) = √3/2, 0°< A + B ≤ 90° and A > B, then find the
measures of angles A and B.
1
29. If tan (A + B) = 3 and tan (A – B) = ; 0° < A+B ≤ 90°; A > B, find A and B.
3
1
30. If sin (A + B) = 1 and sin (A – B) = , 0 ≤ A + B ≤ 90° & A > B, then find A and B.
2
31. Simplify:
32. If θ = 45°, then what is the value of 2 sec2θ + 3 cosec2θ ?
1 1
33. Prove that 2sec2 A
1 sin A 1 sin A
34. Prove the trigonometric identities: (1 + tan² θ) (1 + sinθ) (1 – sinθ) = 1
sin
35. Prove the trigonometric identities: cos ec c ot
1 cos
36. Prove that (sinA + cosecA)2 + (cosA + secA)2 = 7 + tan2A + cot2A
cos A 1 sin A
37. Prove that 2sec A
1 sin A cos A
sin cos 1
38. Prove that: sec tan
sin cos 1
39. Prove that (1 + cot θ – cosec θ) (1 + tan θ + sec θ) = 2
cot A cos A cos ecA 1
40. Prove that
cot A cos A cos ecA 1
cos 2 sin 2
41. Prove that: 1 sin cos
1 tan 1 cot
42. If cos θ + sin θ = √2 cos θ, show that cos θ – sin θ = √2 sin θ.
tan cot
43. Prove that 1 sec cos ec
1 cot 1 tan
cos sin 1
44. Prove that cos ec cot
cos sin 1
2
1 tan 2 A 1 tan A 2
45. Prove that 2 tan A
1 cot A 1 cot A
KRISHNA'S INSTITUTE : 2nd Floor, Jaipuria Plaza, Sec - 26, Noida (U.P) Page - 2-
