Show that:`(frac(sin3theta+2sin5theta+sin7theta)(sintheta+2sin3theta+sin5theta))=cos2theta+sin2thetacot3theta`

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

(sintheta+sin 2theta)/(1+costheta+cos2theta)=

Prove that sin^6theta+cos^6theta=1-3sin^2thetacos^2theta

Prove that (frac(sintheta-2sin^3theta)(2cos^3theta-costheta))=tantheta

sin(pi+theta)sin(pi-theta)cosec^2theta=

|(sin^2theta,cos^2theta),(cos^2theta,sin^2theta)|=

Prove the following: (frac(sin^3theta+cos^3theta)(sintheta+costheta))+(frac(sin^3theta-cos^3theta)(sintheta-costheta))=2