Prove that `(sec8theta-1)/(sec4theta-1)=(tan8theta)/(tan2theta)`

Prove that (1+sec2theta)(1+sec4theta)(1+sec8theta)=(tan8theta)/(tantheta)

Prove that (cos2theta)/(1+sin2theta)=tan(pi//4-theta)

Prove that (sin2theta)/(1+cos2theta)=tantheta

Prove that (sin2theta)/(1-cos2theta)=cottheta

Prove that (costheta)/(1+sintheta)=tan((pi)/(4)-(theta)/(2))

Consider the trigonometric expression sin(2A)/(1-cos 2A) amd sin(2A)/(1+cos 2A) .(iii)Prove that (1-cos theta)/sin theta=tan (theta/2)=(sin theta)/(1+cos theta) .

Prove that sin (3theta)/(1+2cos 2theta)=sin theta .

Given that 1-costheta=2sin^2(theta/2) and 1+costheta=2cos^2(theta/2) prove that (1+sintheta-costheta)/(1+sintheta+costheta)=tan(theta/2)

Prove that (1+sintheta-cos theta)/(1+sin theta+costheta)=tantheta//2

(ii)Prove that tan(pi/4-theta)=(1-tan theta)/(1+tan theta)