$Cosx + \frac{1}{4} {Cos}^{3} x + \frac{1}{5} {Cos}^{5} x + \dots \dots \infty =$

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$\log \tan x$

$\log \cot x$

$\log \tan (x / 2)$

$\log \cot (x / 2)$

answer is D.

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Detailed Solution

Given eqn

$= \frac{1}{2} \log (\frac{1 + \cos x}{1 - \cos x}) = \frac{1}{2} \log (\frac{2 \cos^{2} \frac{x}{2}}{2 \sin^{2} \frac{x}{2}}) = \log c o t \frac{x}{2}$

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