Prove that `sintheta+sin2theta+sin4theta+sin5theta=4cos(theta/2)cos((3theta)/2)sin3theta`

Prove that sintheta+sin3theta+sin5theta+sin7theta=4costhetacos2thetasin4theta

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

Prove that: (sin2theta)/(costheta cos3theta)+(sin4theta)/(cos3theta.cos5theta)+(sin6theta)/(cos5theta.cos7theta)+… to terms = 1/(2sintheta) [sec(2n+1)theta-sectheta]

Prove that: (sin2theta)/(costheta cos3theta)+(sin4theta)/(cos3theta.cos5theta)+(sin6theta)/(cos5theta.cos7theta)+… to terms = 1/(2sintheta) [sec(2n+1)theta-sectheta]

Prove that (sintheta-sin5theta+sin9theta-sin13theta)/(costheta-cos5theta-cos9theta+cos13theta)=cot4theta

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

Prove the following : sin theta+ sin 3 theta+ sin 5 theta+sin 7 theta=4 cos theta cos2 theta sin4 theta .

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

Prove that: sin4 theta=4 sin theta cos^(3)theta-4cos theta sin^(3)theta

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