Prove that `sin(3theta)/sintheta-cos(3theta)/costheta=2`

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

(sintheta+sin2theta)/(1+costheta+cos2theta) =

(sintheta+sin2theta)/(1+costheta+cos2theta)=?

Prove that: cos2theta.costheta/2-cos3theta.cos(9theta)/(2)=sin5theta.sin(5theta)/(2)

Prove that : (sintheta-2sin^(3)theta)/(2cos^(3)theta-costheta)-tantheta

costheta-cos2theta=sin3theta

Prove that : (sintheta)/(1+costheta)+(1+costheta)/(sintheta)=2"cosec"theta

Prove that : (1-costheta)/(sintheta)+(sintheta)/(1-costheta)=2"cosec "theta

Prove that (cos^(3)theta-cos 3theta)/(cos theta)+("sin"^(3)theta+"sin" 3theta)/("sin" theta)=3 .

Prove that : sin theta/cos(3theta) +sin (3theta)/cos (9theta) + sin(9theta)/cos( 27theta )= 1/2(tan27 theta -tan theta)