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

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

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

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

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

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

Prove that (tan 5theta + tan 3theta)/(tan 5theta - tan 3theta) = 4 cos 2theta cos 4theta

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) .

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

(sin 3 theta + sin 5 theta + sin 7 theta + sin 9theta)/(cos 3 theta + cos 5 theta + cos 7 theta + cos 9 theta )=

Prove that (cos theta-sin theta)/(cos theta+sin theta)=sec2theta-tan2theta