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

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

\(\frac{(1-cos\theta)}{(1+-cos\theta)}=tan^2(\frac{\theta}{2})\\ LHS=\frac{(1-cos\theta)}{(1-cos\theta)}=1\ne RHS\\ \mbox{I am guessing that you have writen the question incorrectly.}\)

I think you meant this :

(1-costheta)/(1+costheta)=tan^2(theta/2)

tan ^2 (theta/2)  =

sin^2 (theta/2) / cos^2 (theta/2)  =

 (±√  ( [ 1 - cos theta] / 2 ) )^2 /  (±√ ( [ 1 + cos theta] / 2 ) )^2

( [ 1 - cos theta] / 2 )  /  ( [ 1 + cos theta] / 2)  =

[1 - cos theta] / [1 + cos theta]  =  the left hand side