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

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

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

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

Prove that: (tantheta)/(sectheta -1) = (tan theta + sec theta + 1)/(tan theta + sec theta -1)

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

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

Prove that (2 cos 2 theta+1)/(2 cos 2theta-1)=tan(60^@+theta) (tan 60^@-theta)

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

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 ]

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