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

\int d x / s i n x \cdot s i n (x + α) = ?

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

\int \frac{d x}{s i n x . s i n (x + α)}

\frac{1}{s i n α} \int \frac{s i n {(x + α) - x}}{s i n x . s i n (x + α)} d x

\frac{1}{s i n α} \int \frac{s i n (x + α) c o s x - c o s (x + α) s i n x}{s i n x s i n (x + α)} d x

\frac{1}{s i n α} [\int c o t x - c o t (x + α)] d x

\frac{1}{s i n α} [l n s i n x - l n s i n (x + α)]

\frac{1}{s i n α} l n {\frac{s i n x}{s i n (x + α)}} + c