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

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

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

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

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

Prove that (1 - cos 4theta)/(1 - cos 5theta) = [(sin (2theta))/(sin(5/2theta))]^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 cos^2theta=(1+cos2theta)/2

Prove that (cos(90^(@)+theta)sec(-theta)tan(180^(@)-theta))/(sec(360^(@)-theta)sin(180^(@)+theta)cot(90^(@)-theta))=-1 .

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

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