Prove that the equation `2 sin x+cos x=3` has no solution.

Prove that (sin x+sin 3 x)/(cos x+cos 3 x)=tan 2 x

Prove that (sin 3 x+sin x) sin x+(cos 3 x-cos x)cosx=0

Prove that (sin 5 x+sin 3 x)/(cos 5 x+cos 3 x)=tan 4 x

Prove that sin 2 x+2 sin 4 x+sin 6 x=4 cos ^(2) x sin 4 x

Find the general solutions of sin x+cos x=1 .

Prove that cos^2 2x-cos^2 6x=sin4x sin8x

The solution of the equation [sin x+ cos x]^(1+ sin 2x)=2,-pile x le pi is a) pi/2 b) pi c) pi/4 d) (3 pi)/4