Mathematics

$\int \dfrac{1}{1-cos\dfrac{x}{2}}$ dx

SOLUTION
As we know that

$1-\cos 2\theta=2\sin^2 \theta$

$\displaystyle\int \dfrac{d x}{1-\cos \frac{x}{2}}=\int \dfrac{d x}{2\sin^2 \frac{x}{4}}$

$=\dfrac{1}{2}\displaystyle\int \text{cosec}^2 \frac{x}{4} d x$

$=\dfrac{1}{2}\times \dfrac{1}{\frac{1}{4}}(-\cot \frac{x}{4})+C$

$=-2\cot \dfrac{x}{4}+C$

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Subjective Medium Published on 17th 09, 2020
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 126

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