Solve `e^(sin x)-e^(-sin x) - 4 = 0`.

Explanation

Given that
` e^(sin x) - e^(-sin x) - 4 = 0`.
Let ` e^(sin x) = y`.
Then, given equation becomes
` y-1/y - 4 = 0`
` or y^(2) - 4y-1 = 0`
`:. Y = e^(sin x) = 2 + sqrt5, 2- sqrt5`
Since ` e^(sin x) gt 0, e^(sin x) ne 2 - sqrt5`
Also, maximum value of ` e^(sin x )` is e when sin x = `.
So, ` e^(sin x) ne 2+ sqrt5`
Therefore, given equation has no solution.