Mathematics

Evaluate: $$\displaystyle\int {{{\cos 2x} \over {\sin x}}dx} $$


SOLUTION
$$I=\displaystyle\int \dfrac{\cos 2x}{\sin x}dx$$

$$=\displaystyle\int \dfrac{1-2\sin^2x}{\sin x}dx$$

$$=\displaystyle\int cosec xdx-2\displaystyle\int \sin x dx$$

$$=log|cosec x+\cot x|+2\cos x+c$$.
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Subjective Medium Published on 17th 09, 2020
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