\[\int_{{}}^{{}}{\frac{dx}{5+4\cos x}=}\] [Roorkee 1983; RPET 1997]

\[\frac{1}{3}{{\tan }^{-1}}\left( \frac{1}{3}\tan \frac{x}{2} \right)+c\]

\[\frac{2}{3}{{\tan }^{-1}}\left( \frac{1}{3}\tan x \right)+c\]

\[\frac{1}{3}{{\tan }^{-1}}\left( \frac{1}{3}\tan x \right)+c\]

\[\frac{2}{3}{{\tan }^{-1}}\left( \frac{1}{3}\tan \frac{x}{2} \right)+c\]

\[\int_{{}}^{{}}{\frac{dx}{5+4\cos x}=}\]

1.	\[\int_{{}}^{{}}{\frac{dx}{5+4\cos x}=}\] [Roorkee 1983; RPET 1997]
A.	\[\frac{2}{3}{{\tan }^{-1}}\left( \frac{1}{3}\tan x \right)+c\]
B.	\[\frac{1}{3}{{\tan }^{-1}}\left( \frac{1}{3}\tan x \right)+c\]
C.	\[\frac{2}{3}{{\tan }^{-1}}\left( \frac{1}{3}\tan \frac{x}{2} \right)+c\]
D.	\[\frac{1}{3}{{\tan }^{-1}}\left( \frac{1}{3}\tan \frac{x}{2} \right)+c\]
Answer» D. \[\frac{1}{3}{{\tan }^{-1}}\left( \frac{1}{3}\tan \frac{x}{2} \right)+c\]

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\[\int_{{}}^{{}}{\frac{dx}{5+4\cos x}=}\] [Roorkee 1983; RPET 1997]

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