Class 10 chapter Trigonometry Question Bank
1. Q):- if sin A = \frac{8}{17} , find other trigonometric ratios of \angle A .
2. Q):- if cos A = \frac{9}{41} , find other trigonometric ratios of \angle A .
3. Q):- if tan A = \sqrt{3} , find other trigonometric ratios of \angle A .
4. Q):- if sin \theta = \frac{25}{7} , find other trigonometric ratios of \theta .
5. Q):- if cos \theta = \frac{3}{5} , find the value of ( \frac{5 cosec \theta – 4 tan \theta}{sec \theta + cot \theta} ) .
6. Q):- if sec \theta = \frac{5}{4} , show that \frac{(2 cos \theta – sin \theta)}{(cot \theta – tan \theta)} = \frac{12}{7} .Â
7. Q):- if \triangle ABC it is given that \angle B = {90}^\circ  and AB : AC = 1 : \sqrt{2} . find the value of ( \frac{2 tan A}{1 + tan^2 A} ) .
8. Q):- if 3 tan \theta = 4 , evaluate \frac{3 sin \theta + 2 cos \theta }{3 sin \theta – 2 cos \theta} .
9. Q):- if 5cot \theta = 3 , find the value of ( \frac{5 sin \theta – 3 cos \theta}{4 sin \theta + 3 cos \theta} ) .Â
10. Q):- if 7 sin^2 \theta + 3 cos^2 \theta  = 4 , show that tan \theta = \frac{1}{\sqrt{3}} .
11. Q):- if cot \theta = \frac{15}{8} , then evaluate \frac{(2 + 2 sin \theta)(1 – sin \theta)}{(1 + cos \theta)(2 – 2 cos \theta)} Â
12. Q):- in \triangle ABC right – angled at B , AB = 5 cm and BC = 12 BC . find the values of sin A , sin C , sec A and sec C.
13. Q):- in a \triangle ABC , \angle B = 90^{\circ}  , AB = 5 cm and (BC + AC) = 25 cm . find the value of sin A , cos A , cosec C and sec C .
14. Q):- in a \triangle ABC , \angle B = 90^{\circ} , AB = 7 cm and (AC – BC) = 1 cm . find the value of sin A , cos A , sin C , and cos C.
15. Q):- in a \triangle ABC , \angle C = 90^{\circ} and tan A = \frac{1}{\sqrt{3}} . find the value ofÂ
    (i) sin A . cos B + cos A . sin B  (ii) cos A . cos B – sin A . sin B
16.Q :- If \angle A and \angle B    are acute angle  such that cos A = cos B   then prove that   \angle A =  \angle B. Â
17. Q :- If sin \theta = \dfrac{\sqrt{3}}{2}, find the value of all T – ratio of \theta .Â
18. Q :- If cos \theta =Â \dfrac{\sqrt{7}}{25}, find the values of all T-ratios of \theta .
19. Q :- If tan \theta = \dfrac{15}{8}, find the values of all T-ratios of \theta .Â
20. Q :- If cot \theta = 2, find the values of all T-ratios of \theta .
21. Q :- If cosec \theta = \sqrt{10} , find the value of all T-ratio of \theta Â
22. Q :- If sin \theta = \dfrac{a^2 – b^2}{a^2 + b^2}, find the value of all T-ratios of \theta
23. Q :- If 15 cot A = 8 , find the values of sin A and sec A.Â
24. Q :- If sin A = \dfrac{9}{41} , find the value of cos A and then tan A .Â
25. Q :- If cos \theta = 0.6 , show that (5 sin \theta – 3 tan \theta ).
26. Q :- If cosec \theta = 2, show that cot \theta +Â (\dfrac{sin \theta}{1+cos \theta} ) = 2.
27. Q :- If tan \theta = \dfrac{1}{\sqrt7} , show that \dfrac{cosec^2 \theta – sec^2}{cosec^2 \theta + sec^2 \theta} = \dfrac{3}{4}
28. Q :- If tan \theta = \dfrac{20}{21} , show that \dfrac{1 – sin\theta + cos\theta}{1 + sin\theta + cos\theta} = \dfrac{12}{7}. Â
29. Q :- If cot \theta = \dfrac{3}{4}, show that \sqrt\dfrac{sec \theta – cosec \theta}{sec \theta + cosec \theta} = \dfrac{1}{\sqrt7} .Â
30. Q :- If sin \theta = \dfrac{3}{4} , show that \sqrt\dfrac{cosec^2 \theta – cot^2 \theta}{sec^2 \theta – 1} = \dfrac{\sqrt7}{3}. Â
31. Q :- If sin \theta = \dfrac{a}{b}, show that (sec \theta + tan\theta ) = \sqrt\dfrac{b + a}{b – a}. Â
32. Q :- If cos \theta = \dfrac{3}{5} , show that \dfrac{sin \theta – cot \theta}{2tan\theta} = \dfrac{3}{160}. Â
33. Q :- If tan \theta = \dfrac{4}{3} , show that (sin\theta + cos \theta) = \dfrac{7}{5} .Â
34. Q :- If tan \theta = \dfrac{a}{b}, show that (\dfrac{a sin\theta – b cos \theta}{ a sin\theta + b cos \theta})Â = (\dfrac{a^2Â –Â b^2}{a^2Â +Â b^2}) .
35. Q :- If 3 tan \theta = 4 , show that (\dfrac{4 cos \theta – sin \theta}{2 cos \theta + sin \theta }) = \dfrac{4}{5}. Â
36. Q :- If 3cot \theta = 2 show that  (\dfrac{4sin \theta – 3cos \theta}{2sin \theta + 6cos \theta }) = \dfrac{1}{3} . Â
37. Q :- If 3 cot \theta = 4 , show that \dfrac{3 – 4tan^2 \theta}{4tan^2 \theta – 3 } = (cos^2 \theta – sin^2 \theta ) .
38. Q :- If sec \theta = \dfrac{17}{8},  verify that ( \dfrac{3 – 4 sin^2 \theta}{4cos^2\theta – 3 } = (\dfrac{3 – tan^2 \theta}{1 – 3tan^2 \theta }) .Â
39. Q :- In a \Delta ABC, \angle BÂ = 90 \degree AB = 24 cm and BC = 7 cm.Â
Find (i) sin A  (ii) cos A  (iii) sin C  (iv)  cos C. Â
40. Q :- In a \Delta ABC, \angle C = 90 \degree , \angle ABC = \theta , , BC = 21 units and AB = 29 units.Â
show that (cos^2 \theta – sin^2 \theta ) = \dfrac{41}{841}.
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