2 x ^2 x d x - Vidyadip

Question

$\int \frac{\cos 2 x}{\sin ^2 x} d x$

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Answer

$\int \frac{\cos 2 x}{\sin ^2 x} d x$
$=\int \frac{1-2 \sin ^2 x}{\sin ^2 x} d x \quad \ldots \ldots\left[\because \cos 2 \theta=1-2 \sin ^2 \theta\right]$
$=\int\left(\frac{1}{\sin ^2 x}-\frac{2 \sin ^2 x}{\sin ^2 x}\right) d x$
$=\int\left(\operatorname{cosec}^2 x-2\right) d x$
$=-\cot x-2 x + c $

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