TRIGNOMETRY CLASS 11 DPP
TRIGNOMETRY
1. Prove that
sin20. sin40. sin60. sin80 = 3/16
2. Prove that
cos15 cos30. cos45. cos60. cos75 = 3/16
3. Express as Product
1) sin5x + sin3x 2) cos6x - cos8x
3) sin2x - sin4x 4) cosx + cos7x
3. Express as the sum
1) 2 sinx sin3x 2) cosx sin2x
3) 4 sin6x sin2x
4. Prove that
sin²π/6 + cos²π/3 - tan²π/4 = -1/2
5. 2sin²π/6 + cosec²7π/6 . cos²π/3 = 3/2
6. Find the value of
1) sin75 2) tan15
7. Prove that
cos(n+1)x cos(n+3)x + sin(n+1)x sin(n+3)x = cosx
8. Prove that
sin5x + sin3x / cos5x + cos3x = tan4x
9. Prove that
(Cos4x+ Cos2x + Cos3x )/(Sin4x + Sin 2x+ Sin3x )= cot3x
10. tan4x= 4 tanx ( (1-〖tan〗^2 x))/(1-〖6tan〗^2 x+〖tan〗^4 x)
11. Prove that
(Sin3x – Sinx) / (Cos2x – Sin2x) = 2Sin x
12. Cos9x – Cos5x / Sin17x – Sin3x = -Sin2x / Cos 10x
13. Prove that
(1-cos4x) + sin4x / (1+ cos4x) + sin4x = tan2x
14. (Sinx + Siny)2 + (Cosx + Cosy)2 = 4 Cos2(x-y/2)
15. Prove that
tan (60-x) . tanx . tan (60+x) = tan3x.
16. Prove that
Cos²n + Cos²(n+π/3) + Cos²(n-π/3) = 3/2
17. Find the value of tan(π/8)
18. Prove that
Cos 2x Cos x/2 - Cos 3x Cos 9x/2 = Sin5x. Sin 5x/2
19. Prove that
Cos4x = 1-8Sin²x . Cos²x
20. Prove
Cos6x = 32 Cos⁶x - 48Cos⁴x + 18Cos²x - 1
21. Prove that
Cos((3π/4) + x) - Cos((3π/4) - x) = - √2Sinx
22. Prove that
Sinx - Sin3x / Sin2x – Cos2 = 2Sinx
23. Find the value of
Sin 765° Cos(-1410°)
24. Find the value of
1) cot((-15π)/4)
2) sin((-11π)/2)
25. If tanx = -5/12, x ∈ 4th. Find other trigonometrical function
26. Find the value of Cos(-1710°)
27. Convert into radian
1) 40° 20’ 2) -47°30’
28. Convert into degree
1) 11/6 2) -4
29. A wheel makes 360 revolution in 1 minute. Through how many
radian does it turn in one second.
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