The number of solutions, of the equation e ^ x - 2 e ^ - x = 2 is

Let, ${e}^{\sin x} = t$

$⇒ t - \dfrac{2}{t} = 2$

$⇒ {t}^{2} - 2t - 2 = 0$

$⇒ {t}^{2} - 2t + 1 = 3$

$⇒ {\left(t - 1\right)}^{2} = 3$

$⇒ t = 1 \pm \sqrt{3}$

$⇒ t \approx 2 . 73, - 0 . 73\left(\text{not possible}\right)$

$⇒ t \approx 2 . 73$

$⇒ {e}^{\sin x} \approx 2 . 73$

$⇒ \sin x \approx \log_{e}\left(2 . 73\right)$

$⇒ \sin x > 1 \to \text{Not possible}$

So no solutions will be possible for the given equation.