SSVM WORLD SCHOOL
CLASS-X WORKSHEET- TRIGONOMETRY
1.Find the value of tan 60° geometrically.
2. If tanA +1 =√2, then prove that cosA – sinA =√2 sinA
1 1 𝑡𝑎𝑛𝐴+𝑡𝑎𝑛𝐵
3. If A and B are acute angles such that tanA = , tanB = and tan(A +B)=
2 3 1−𝑡𝑎𝑛𝐴𝑡𝑎𝑛𝐵
4. Given that sin (A + B) =sin A cos B + cos A sin B, find the value of 75°.
5. If tan θ +sinθ =m and tanθ –sinθ=n show that .
6. Prove that
7. Prove that = cosecA + cot A
8. If √3 tanθ = 3 sinθ, find the value of .
9.If cosecA + cotA =2 , then find the value of sinA and tanA.
10. Prove that siny + siny cot2y = cosecy
11. If a cos θ-bsinθ =c prove that (a sinθ + bcosθ) =±√𝑎2 + 𝑏 2 − 𝑐 2
12. Prove that
13. If 5 tanθ =4 , find the value of
14. If 1 + sin2x = 3 sinx cosx, then prove that tanx = 1 or tan x = ½.
15. If sin( A-B) =1/2 and cos (A+B) =1/2, 0°<( A+B) 90°, A> B. Find A and B
16. Prove that
17. If 3 cotA =4, find the value of
18. The value of cos1˚cos2˚ cos3˚cos4˚ cos5˚ ………………………cos90˚
19. If the angles of ∆ABC are in the ratio 1:1:2, respectively the largest angles being angle C, then find the value
𝑠𝑒𝑐𝐴 𝑡𝑎𝑛𝐴
of - .
𝑐𝑜𝑠𝑒𝑐𝐵 𝑐𝑜𝑡𝐵
20. Prove that sinA (1+tanA) +cosA (1+cot A)= secA+ cosecA
21. Prove that
√3 1
22. Find A and B , if sin(A + 2B) = , and cos ( A + B ) =
2 2
23. If tan θ =1/√7, find the value of
24. If tan (A-B) =1/√3 and sin (A +B) =√3/2 , 0° A> B. find A and B.
25. Prove that :
26. If cosecθ= , prove that cosecθ + cotθ =2x or 1/2x
27. Show that tan4 A + tan2A = sec4A – sec2A
28. Prove that :1+
29. If √3 sinθ – cosθ = 0 and 0˚<θ<90˚, find the value of θ.
30. If and prove that
31. If cosec (A –B )=2 , cot (A+B) = 1/√3, 0°< ( A+ B )< 90° , A> B , then find A and B.
32. Show that
33. If sin (A +B) =√3/2, cos (A – B) =√3/2, 0< A+B < 90° , A+B find A and B.
34. Prove that (cosecA – sin A )( sec A – cos A) =
35. If tan A =√2 -1 , show that sinA cosA =√2/4
36. Prove that
37. Prove that
38. Prove that
39. Prove that
40. Prove that .
41. Prove that : Sin A(1+tanA)+ cos A(1+cotA)=secA +cosec A
42. If tanA =1/√3,ΔABC is right angled at B. Find the value of sin A cos C + cos A sinC.
43. Prove that
44.Prove that
45. If x=r sinA cosC, y=r sinA sinC, z=r cosA, prove that r²=x²+y²+z²
46. If cosθ –sinθ =√2sinθ prove that cosθ + sinθ =√2 cosθ.
47 . If θ=30° , verify that cos2θ=1- tan²θ/ 1-tan²θ
48. If (secθ + tanθ) =p prove that sinθ =
49. Prove that
50. Prove that
51. Prove that
52. If θ =30˚ verify that cos2θ=
53. Prove that
54. Find the value of tan60° geometrically.
55. Prove that
56.Evaluate tan²45°+3sin²60°
57.Prove that : 1+
58. Prove that
59.Show that
60. Prove that :
