Question

evaluate integration sin2x/(sinx)²

please help.... ​

Answer 1

\displaystyle \int \bf \: \frac{sin2x}{ {(sin \: x)}^{2} } \: dx \\ = \displaystyle \int \bf \: \frac{2 \: sin \: x \: \: cox \: x}{sin \: x \: \: sin \: x} \: dx \\ =2 \displaystyle \int \bf \: \frac{cos \: x}{ \: sin \: x} \: dx \\ \\ \sf \: substitute \: \: u \: = \: sin \: x \\ \bf \therefore \: \: \: \: \: \: \: \: \: \: \: \: du \: = cos \: x \: dx\\ \\ = 2\displaystyle \int \bf \: \frac{1}{u} du \\ = 2 \bf \: ln |u| + c \\ = 2 \bf \: ln |sin \: x| + c