Mathematics

# $\displaystyle \int \frac{cosec x}{\log \tan \left ( x/2 \right )}dx$

##### ANSWER

$\displaystyle \log \left [ \log \tan \left ( x/2 \right ) \right ].$

##### SOLUTION
Let $\displaystyle I=\int \frac{cosec x}{\log \tan \left ( x/2 \right )}dx$
Put $\displaystyle \log \tan \left( x/2 \right) =t\Rightarrow \cos \sec xdx=dt$
Therefore
$\displaystyle I=\int { \frac { dt }{ t } } =\log { t } =\log \left[ \log \tan \left( x/2 \right) \right]$
Hence, option 'A' is correct.

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Single Correct Medium Published on 17th 09, 2020
Questions 203525
Subjects 9
Chapters 126
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