Question

Find the number of solutions of the equation $e^{\sin x}-e^{-\sin x}-4=0$

Answer 1

Put $e^{\sin x}=t$ $\Rightarrow$ $t^2-4t-1=0$

$\Rightarrow$ $t=e^{\sin x}=2\pm \sqrt{5}$

Now $\sin xϵ[-1,1]$.Thus

$e^{\sin x}ϵ[e^{-1},e^1]$ and $2\pm \sqrt{5}\text{/}ϵ[e^{-1},e^1]$

Hence, there does not exist any solution.
Ans: 0