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Question Number 44148 by LXZ last updated on 22/Sep/18

$$\int dx/sinx\cdot sin(x+\alpha )=?$$

Answered by tanmay.chaudhury50@gmail.com last updated on 22/Sep/18

$$\int \frac{dx}{sinx.sin(x+\alpha )}$$$$\frac{1}{sin\alpha }\int \frac{sin\{(x+\alpha )-x\}}{sinx.sin(x+\alpha )}dx$$$$\frac{1}{sin\alpha }\int \frac{sin(x+\alpha )cosx-cos(x+\alpha )sinx}{sinxsin(x+\alpha )}dx$$$$\frac{1}{sin\alpha }[\int cotx-cot(x+\alpha )]dx$$$$\frac{1}{sin\alpha }[lnsinx-lnsin(x+\alpha )]$$$$\frac{1}{sin\alpha }ln\left\{\frac{sinx}{sin(x+\alpha )}\right\}+c$$

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