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

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

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

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

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

Prove that y=(4 sin theta)/((2+cos theta))-theta is an increasing function of theta in [0, pi/2] .

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

Prove that cos^2theta=(1+cos2theta)/2

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

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) .