Lesson = 3 [ Trigonometric Functions ] Important Questions

 

Q.1. Prove that cos 510° cos 330° + sin 390° cos 120° = –1.

Q.2. Find the maximum and minimum value of 7 cos x + 24 sin x.

Q.3. Find the value of √3 cosec 20° – sec 20°.

Q.4. Show that tan 3x tan 2x tan x = tan 3x – tan 2x – tan x.

Q.5. Solve sec x. cos 5x + 1 = 0

Q.6. Prove that : cos A cos 2A cos 4A cos 8A = sin16A / 16.sinA  . 

Q.7. If α and β are the solution of the equation a tanӨ + b secӨ = c then show that tan ( α + β ) = 2ac / a² - c².  

Q.8. If sin ( Ө + α ) = a  and sin (  Ө + β ) = b then prove that cos 2( α - β ) - 4ab cos ( α - β ) = 1-2a² - 2b².

Q.9. sin x  - 3sin 2x  + sin 3x =  cos x - 3cos 2x +cos 3x.

Q.10. Cos² x + Cos² ( x + π/3 ) + Cos² ( x - π/3 ) = 3/2.

 

Q.11. Solve 2tan²  x + sec² x = 2.

Q.12. If sec x=  √2 and  3π/2 < x < 2π find the value of 1 – tan x  – cosec x / 1 – cot x -  cosec x.

Q.13. Prove that sin 10° sin 30° sin 50° sin 70° = 1 /16 . 

Q.14. Prove that tan 13x = tan 4x + tan 9x + tan 4x tan 9x tan 13x.

Q.15. Prove that tan 70° = tan 20° + 2 tan 50°

Q.16. Show that 2 sin2 β + 4 cos (α + β) sin α sin β + cos 2 (α + β) = cos 2α  

cos 10° + cos 110° + cos 130° = 0.

Q.17. Find the value of tan 225° cot 405° + tan 765° cot 675°.

Q.18. tan 560 =   

Q.19. Find the value of tan π/8 .

Q.20. Prove that Cos 6x= 32 Cos6x – 48 Cos4 x + 18 Cos2 x-1

Lesson =1 [ Sets ] Important Questions

Q.21. Prove that Sin 2x - Sin 4x + Sin 6x = 0

Q.22. Prove that tan 4x = 4 tan x ( 1 - tan² x ) / 1 - 6 tan² x + tan⁴ x.

Q.23. Prove that (Cos x + Cos y)2 + (Sin x – Sin y)2 = 4 Cos2 ( X + Y / 2 ).

Q.24. Prove that Sin x + Sin 3x + Sin 5x + Sin 7x = 4 Cos x. Cos 2x. Sin 4x.

Q.25. Prove that Cot 4x (Sin 5x + Sin 3x) = Cot x (Sin 5x – Sin 3x).

Q.26. Find the general solution of sin2x + sin4x + sin6x = 0.

Q.27. If Sin α + Sin β = a and Cos α + Cos β = b show that Cos (α + β) = b² - a² / b² + a² .

Q.28. Prove that Cos α + Cos β + Cos γ + Cos (α + β + γ) = 4 cos ( α + β / 2 ) . cos ( β + γ / 2 ) . cos ( γ + α / 2 ).

 

Q.29. Prove that 

Q.30. Prove that 

Q.31. Prove that Cos 200. Cos 400. Cos 600 Cos 800 = 1 / 16.

Q.32. If cos (α + ) =4/5 and sin (α- )=5/13 , where α lie between 0 and π/4, then find the value of tan 2α.

Q.33. If sin A = $\frac{-5}{13}$, π < A < $\frac{3\pi }{2}$ and cos B = $\frac{3}{5}$, $\frac{3\pi }{2}$ < B < 2π, find cos (A – B).

Q.34. Prove that (sin θ + sec θ)2 + (cos θ  + cosec θ)2 = (1 + cosec θ sec θ)2

Q.35. Prove that cosA + cosB - cosC = 4 cos$\frac{A}{2}$ cos$\frac{B}{2}$ sin $\frac{C}{2}$ – 1

Q.36. Prove that tan(45 + x) = sec 2x + tan 2x.

Q.37. Prove that tan 2x tan x / tan 2x - tan x = sin 2x.

Q.38.sin ( x+y) - 2sin x + sin ( x-y ) / cos ( x+y ) - 2cos x + cos ( x-y ) = tan x.

Q.39. cos 10° + cos 110° + cos 130° = 0.

 

Q.40. tan α. tan ( 60°- α ). tan ( 60° + α ) = tan 3α.