Evaluate the following integrals: 1 1- 2x dx - Vidyadip

Question

Evaluate the following integrals:
$\int\frac{1}{1-\cos2\text{x}}\text{dx}$

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Answer

$\int\frac{1}{1-\cos(2\text{x})}\text{dx}$ $\Big[\therefore\ 1-\cos\text{A}=2\sin^2\Big(\frac{\text{A}}{2}\Big)\Big]$
$=\int\frac{\text{dx}}{2\sin^2\text{x}}$
$=\frac{1}{2}\int\text{cosec}^2\text{x dx}$
$=\frac{1}{2}[-\cot\text{x}]+\text{C}$
$=-\frac{1}{2}\cot\text{x}+\text{C}$

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