Question

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

Answer 1

See below

Explanation:

`(sin3x+sinx)sinx+(cos3x-cosx)cosx`

`=sin3xsinx+sin^2x+cos3xcosx-cos^2x`

`=sin3xsinx+cos3xcosx-(cos^2x-sin^2x`

`=cos2x-cos2x`

`0`, as required