Mathematics

Evaluate $$\displaystyle\int { \dfrac { \sin { x }  }{ \sin { (x+a) }  } dx } $$


SOLUTION
$$\displaystyle\int \dfrac{\sin x}{\sin (x+a)}d x$$

$$=\int \dfrac{\sin (x+a-a)}{\sin (x+a)}d x$$

$$=\int \dfrac{\sin (x+a)\cos a-\cos(x+a)\sin a}{\sin (x+a)}d x$$

$$=\cos a\int d x-\sin a\int \cot (x+a)d x$$

$$=x\cos a+\sin a\log \cos (x+a)+C$$
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Subjective Medium Published on 17th 09, 2020
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