IIT JEE 1982 Maths - 'Adapted' - Subjective to Multi-Correct Q3

Let $e^{\sin x}$ be $y$ , $y-\frac{1}{y}-4=0$ $y^2-1-4y=0$ $y=2\pm \sqrt{5}$ $e^{\sin x}=2\pm \sqrt{5}$ By taking $\log$ both the sides, $\sin x=\log _e\left(2\pm \sqrt{5}\right)$ As by observation $1<\left(2+\sqrt{5}\right)$ so $x=\sin ^{-1}\left(2+\sqrt{5}\right)$ is incorrect,

Coming to another solution, $x=\sin ^{-1}\left(2-\sqrt{5}\right)$ doesn't exists as log of negative numbers are undefined.

So neither of our solution divides the given options hence the answer is 9999.