27 cos5 θsin3 θ=
6sin 2θ+2 sin 4θ-2 sin6θ-sin 8θ
6sin 2θ-2 sin 4θ-2 sin6θ-sin 8θ
6sin 2θ+2 sin 4θ+2 sin6θ+sin 8θ
6sin 2θ-2 sin 4θ-2 sin6θ+sin 8θ
If 16 sin5 θ=asin 5 θ+b sin 3θ+c sin θ then
2
4
6
8
16 cos5 θ=
cos 5θ+5 cos 3θ+10 cosθ
cos 5θ-5 cos 3θ+10 cosθ
cos 5θ+5 cos 3θ-10 cosθ
cos 5θ-5 cos 3θ-10 cosθ
If cos α+ cos β=0= sin α + sin β then cos(α - β)=
0
1
-1
The last terms in the expantions of sin 8θ, sin 9θ respectively are
8cos θ.sin7 θ,-sin9 θ
8cos θ.sin7 θ,sin9 θ
-8cos θ.sin7 θ,-sin9 θ
-8cos θ.sin7 θ,sin9 θ
If sin 6θ=32cos5 θsin θ-32cos3 θsin θ+3x, then x=
cos θ
cos 2θ
sin θ
sin 2θ
32cos4 θ.sin2 θ=
2+2cos 2θ-2cos 4θ-cos 6θ
2-2cos 2θ-2cos 4θ-cos 6θ
2+2cos 2θ+2cos 4θ-cos 6θ
2+2cos 2θ+2cos 4θ+cos 6θ
27 cos8 θ=
cos 8θ+8cos 6θ+28cos 4θ+56cos 2θ+35
cos 8θ+8cos 6θ-28cos 4θ+56cos 2θ+35
cos 8θ-8cos 6θ+28cos 4θ-56cos 2θ+35
cos 8θ+8cos 6θ-28cos 4θ-56cos 2θ+35
27. Cos3 θsin5 θ=
sin 8θ-2sin 6θ-2sin 4θ+6sin 2θ
sin 8θ+2sin 6θ+2sin 4θ+6sin 2θ
cos 8θ-2cos 6θ-2cos 4θ+6cos 2θ
cos 8θ+2cos 6θ+2cos 4θ+6cos 2θ
If sin 6θ=a cos5 θsin θ+bcos3 θsin3 θ+c cos θsin3 θ then a+b+c=
-4
-8
If cos 5θ=a cos θ+bcos3 θ+c cos5 θ+d, then
a=20
b=-25
c=16
d=5
8sin4θ=
cos 4θ-4cos 2θ+3
cos 4θ-4cos 2θ-3
cos 4θ+4cos 2θ+3
cos 4θ+4cos 2θ-3
64cos3 θsin4 θ=
cos 7θ+cos 5θ-3cos 3θ+3 cos θ
cos 7θ-cos 5θ-3cos 3θ+3 cos θ
cos 7θ-cos 5θ-3cos 3θ-3 cos θ
cos 7θ+cos 5θ-3cos 3θ-3 cos θ
64cos7 θ=
cos 7θ-7cos 5θ+21cos 3θ+35cos θ
cos 7θ-7cos 5θ-21cos 3θ-35cos θ
cos 7θ-7cos 5θ+21cos 3θ-35cos θ
cos 7θ+7cos 5θ+21cos 3θ+35cos θ
If a sinx=b cosx= 2ctanx/1-tan2 x then (a2-b2)2/a2+b2=
c2
2c2
3c2
4c2
A= cos 200- sin 200, B= cos 1000+ sin 1000, C= cos 5π/6+ sin 2π/3 then the ascending order is
A,C,B
A,B,C
B,C,A
C,B,A
128 sin8 θ=