Prove that `[1+costheta]/sintheta=cot[theta/2]`

Prove that (1+costheta+sintheta)/(1-costheta+sintheta)=cot(theta/2)

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

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

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

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

Prove that, 1/(costheta-cos3theta)+1/(costheta-cos5theta)+1/(costheta-cos7theta)+…+to n terms = 1/(2sintheta) [cottheta-cot(n+1)theta]

Prove that, 1/(costheta-cos3theta)+1/(costheta-cos5theta)+1/(costheta-cos7theta)+…+to n terms = 1/(2sintheta) [cottheta-cot(n+1)theta]

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

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

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