Prove that `sqrt((1+sintheta)/(1-sintheta))= sec theta + tantheta`

Prove that : sqrt((1-sin theta)/(1+sin theta))= {(sec theta- tan theta, if -pi/2 < theta< pi/2), (-sec theta+ tan theta, if pi/2 < theta< (3 pi)/2):} .

Prove that 1/(1+sintheta)+1/(1-sintheta)=2sec^2theta .

Prove that (1-sintheta)/(1+sintheta)=(sectheta-tantheta)^2 .

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

Prove that (sectheta+tantheta)(1-sintheta)=costheta .

Prove that sintheta/(1-costheta)=cosectheta+cottheta .

Prove that (1+tan^2theta)(1-sintheta)(1+sintheta)=1 .

Prove that (sintheta-2sin^3theta)/(2cos^3theta-costheta)=tantheta .

Prove the following identity : 1/(sec theta-tan theta)= (1+sin theta)/(cos theta) = sec theta+tan theta .

Prove the following identity : 1/(sec theta+tan theta)= (1-sin theta)/(cos theta) = sec theta-tan theta .