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

(sin3theta+sin5theta+sin7theta+sin9theta)/(cos3theta+cos5theta+cos7theta+cos9theta)=

(sin3theta+sin5theta+sin7theta+sin9theta)/(cos3theta+cos5theta+cos7theta+cos9theta)=?

(sin3theta+sin5theta+sin7theta+sin9theta)/(cos3theta+cos5theta+cos7theta+cos9theta) is equal

(sin3 theta+sin5 theta+sin7 theta+sin9 theta)/(cos3 theta+cos5 theta+cos7 theta+cos9 theta)

Prove that (sin theta sin9theta+sin 3 thetasin5 theta)/(sinthetacos 9theta+sin3theta cos5theta)=tan 6 theta

Prove the following : (sintheta+sin3theta+sin5theta+sin7theta)/(costheta+cos3theta+cos5theta+cos7theta) = tan4theta

(sin 3theta+sin5theta+sin7theta+sin9theta)/(cos 3theta+cos 5theta+cos 7theta+cos9theta) is equal to

(sin 3theta+sin5theta+sin7theta+sin9theta)/(cos 3theta+cos 5theta+cos 7theta+cos9theta) is equal to

(sin5theta+sin2theta-sintheta)/(cos5theta+2cos3theta+2cos^2theta+costheta) is equal to

(b)Show that (sin theta+sin 3theta+sin 5 theta+sin 7 theta)/(cos theta+cos3theta+cos 5 theta+cos 7 theta)=tan 4 theta .