PRACTICE QUESTIONS (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°.
Prepared by: M. S. KumarSwamy, TGT(Maths) Page - 1-
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°.
Prepared by: M. S. KumarSwamy, TGT(Maths) Page - 1-
