question_answer

\[2{{\tan }^{-1}}\left[ \sqrt{\frac{a-b}{a+b}}.\tan \frac{\theta }{2} \right]=\]

A)  \[{{\cos }^{-1}}\left( \frac{a\cos \theta +b}{a+b\cos \theta } \right)\]      

B)  \[{{\cos }^{-1}}\left( \frac{a+b\cos \theta }{a\cos \theta +b} \right)\]

C)  \[{{\cos }^{-1}}\left( \frac{a\cos \theta }{a+b\cos \theta } \right)\]           

D)  \[{{\cos }^{-1}}\left( \frac{b\cos \theta }{a\cos \theta +b} \right)\]

E)  None of these