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

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

Prove that (1+sin2theta)/(1-sin2theta)=((1+tantheta)/(1-tantheta))^2

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

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

Prove that sqrt(cot^(2)theta-cos^(2)theta)=cottheta.costheta

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

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

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

Prove that (sin theta -cos theta+1 )/( sin theta + cos theta -1) =(1)/( sec theta -tan theta ) [use the identity sec ^(2) theta =1 +tan ^(2) theta ]