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
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