Question

Sin3x-sinx/cos3x-cosx=-cot2x

Answer 1

Reduce terms: (sin x + sin 3x)/(cos x - cos 3x) =cos(2x)/sin (2x)

(sin x + sin 3x)/(cos x - cos 3x) = cot (2x)

The last line proves the identity (sin x + sin 3x)/(cos x - cos 3x) = cot (2x)