Answer
$e^{x+2\ln |\sin x|}=e^{x}\sin ^2 x$
Work Step by Step
Need to verify $e^{x+2\ln |\sin x|}=e^{x}\sin ^2 x$
Consider left hand side : $e^{x+2\ln |\sin x|}=e^{x} \cdot e^{2\ln |\sin x|}$
Since, $2 e^{a}=e^{a^2}$
Also, $e^{\log x}=x$
Thus, we have $e^{x} \cdot e^{\ln |\sin^2 x|}=e^{x} \cdot \sin ^2 x$
Therefore, $e^{x+2\ln |\sin x|}=e^{x}\sin ^2 x$
Hence, the left-hand side and right hand side are equal.
