Prove that : `(sin theta + sin 3theta + sin 5theta)/(cos theta + cos 3theta + cos 5theta) = tan 3theta`

Prove that : (sin 5theta - 2 sin 3theta + sin theta)/(cos 5theta -cos theta) = tan theta

Prove that : (sin theta + 2 sin 3theta + sin 5theta)/(sin 3theta + 2 sin 5theta + sin 7theta) = (sin 3theta)/(sin 5theta)

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

Prove that : (cos 4theta + cos 3theta + cos 2theta)/(sin 4theta + sin 3theta + sin 2theta) = cot 3theta

Prove that : (cos theta)/(1-tan theta) + (sin theta)/(1-cot theta) = sin theta + cos theta

Prove that (sin 3 theta)/( sin theta) - (cos 3 theta)/(cos theta) = 2

(sin theta + sin 2 theta)/( 1 + cos theta + cos 2 theta) = tan theta.

sin^(3)theta + sin theta - sin theta cos^(2)theta =

Prove that cos^6 theta+ sin^6 theta= 1-3sin^2 theta cos^2 theta

Prove that : sin theta cos^3 theta - cos theta sin^3 theta = 1/4 sin4theta .