The equation $e^{\sin x}-e^{-\sin x}-4=0$ has

The correct option is C No real roots

$e^{\sin x}-e^{-\sin x}-4=0$

Let $e^{\sin x}=t$

So, we get the following equation

$t+\frac{1}{t}=4$

$\Rightarrow t^2-4t-1=0$

$\Rightarrow t=2+\sqrt{5}$ or $2-\sqrt{5}$

$e^{\sin x}=2+\sqrt{5}$ and $2-\sqrt{5}$ is not possible.

Hence, no solution exists.