Answer
$e^{\sin^2 x}e^{\cos^2 x}=e$
Work Step by Step
Need to verify $e^{\sin^2 x}e^{\cos^2 x}=e$
Consider left hand side : $e^{\sin^2 x}e^{\cos^2 x}=e^{\sin^2 x+\cos^2 x}$
We know that $2 e^{a}=e^{a^2}$
Also, $e^{\log x}=x$;
Now, use trigonometric identity such as: $\sin^2 x+\cos^2 x=1$
Then, we have $e^{\sin^2 x+\cos^2 x}=e^{1}$
Thus, $e^{\sin^2 x}e^{\cos^2 x}=e$
Hence, the left-hand side and right hand side are equal.
