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

Prove that : (1-costheta)/(sintheta)+(sintheta)/(1-costheta)=2"cosec "theta

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

Prove that: sqrt((1-sintheta)/(1+sintheta))=sectheta -tan theta .

Prove that: sqrt((1-sintheta)/(1+sintheta))= sec theta- tan theta when (-pi/2) < theta < pi/2 and -sec theta+tan theta when pi/2< theta< (3pi)/2

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

Prove that (cos theta-sintheta)/(cos theta+sintheta)=sec 2 theta-tan 2theta .

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

Prove that : (sintheta)/(1+costheta)+(1+costheta)/(sintheta)=2"cosec"theta

Prove that : (1+sintheta)/(costheta)+(costheta)/(1+sintheta)=2sectheta

Prove that sqrt((1+sintheta)/(1-sin theta))=sectheta+tantheta .