\[{{\cos }^{-1}}\left( \frac{3+5\cos x}{5+3\cos x} \right)\] is equal to [Kerala (Engg.) 2005]

\[{{\tan }^{-1}}\left( \tan \frac{x}{2} \right)\]

\[{{\tan }^{-1}}\left( \frac{1}{2}\tan \frac{x}{2} \right)\]

\[2{{\tan }^{-1}}\left( 2\tan \frac{x}{2} \right)\]

\[\frac{1}{2}{{\tan }^{-1}}\left( 2\tan \frac{x}{2} \right)\]

\[2{{\tan }^{-1}}\left( \frac{1}{2}\tan \frac{x}{2} \right)\]

\[{{\cos }^{-1}}\left( \frac{3+5\cos x}{5+3\cos x} \right)\] is equal

1.	\[{{\cos }^{-1}}\left( \frac{3+5\cos x}{5+3\cos x} \right)\] is equal to [Kerala (Engg.) 2005]
A.	\[{{\tan }^{-1}}\left( \frac{1}{2}\tan \frac{x}{2} \right)\]
B.	\[2{{\tan }^{-1}}\left( 2\tan \frac{x}{2} \right)\]
C.	\[\frac{1}{2}{{\tan }^{-1}}\left( 2\tan \frac{x}{2} \right)\]
D.	\[2{{\tan }^{-1}}\left( \frac{1}{2}\tan \frac{x}{2} \right)\]
E.	\[{{\tan }^{-1}}\left( \tan \frac{x}{2} \right)\]
Answer» E. \[{{\tan }^{-1}}\left( \tan \frac{x}{2} \right)\]

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\[{{\cos }^{-1}}\left( \frac{3+5\cos x}{5+3\cos x} \right)\] is equal to [Kerala (Engg.) 2005]

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