Prove that `sin^3 theta + sin^3 3theta + sin^3 5 theta+....+ n` terms is equal to

Prove that : sin 3 theta=3 sin theta-4 sin^3 theta .

Prove that (sin theta + sin 3theta+ sin 5 theta + sin 7theta)/(cos theta + cos 3theta + cos 5 theta + cos 7theta) = (tan 3theta + tan theta)/(1 - tan 3theta 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^2 theta+sin^2 2theta+sin^2 3theta+....+sin^2 n theta=n/2-(sin n theta cos(n+1)theta)/(2sin theta)

If 3 sin theta + 4 cos theta = 5 , then 3 cos theta - 4 sin theta is equal to?

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

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

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

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