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 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+sin3 theta+sin5 theta)/(cos theta+cos3 theta+cos5 theta)=tan3 theta

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

(sin5 theta-2sin3 theta + sin theta) / (cos5 theta-cos theta) = tan theta

Prove the following identities : (sin theta +sin 3 theta + sin 5 theta + sin 7theta)/(cos theta + cos 3 theta + cos 5 theta + cos 7 theta)=tan 4 theta

(sin theta+sin3 theta+sin5 theta)/(cos theta+cos3 theta+cos5 theta)=tan3 theta

Prove that :(sin5 theta-2sin3 theta+sin theta)/(cos5 theta-cos theta)=tan theta

Prove that (sin theta+ sin 2theta + sin 3 theta)/(costheta+cos2theta+cos3theta)=tan 2 theta