The number of real roots of the equation 
$$e^{\sin x}-e^{-\sin x}-4=0$$

Let $e^{\sin x}=y$
Then $$y-\frac 1y -4=0$$
$$y^2-4y-1=0$$
$$y=2+\sqrt 5 , 2-\sqrt 5$$
How should I solve further ?

$e^{\sin x}-e^{-\sin x}-4 \le e-e^{-\sin x}-4<0.$ Hence, the equation has no real roots !
