prove that `(1-costheta)/sintheta=tan(theta/2)`

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

If costheta-sintheta=sqrt(2)sintheta , then prove that: costheta+sintheta=sqrt(2)costheta

If costheta +sin theta= sqrt(2)cos theta , then prove that costheta-sintheta =sqrt(2)sin theta

Prove that : (1+costheta- sin^(2)theta)/(sintheta+sinthetacostheta)=cottheta

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

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

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

Prove the following Identities (1+sin theta-costheta)/(1+ sintheta+costheta)= tan(theta/2)

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

(i) ("sin"theta "tan"theta)/(1-costheta)=1sectheta (1+costheta)/(1-costheta)=("tan"^2theta)/((sectheta-1))^2