Question

The number of real roots of the equation $e^{sinx}-e^{-sinx}-4=0$ are

• A. 1
• B. 2
• C. Infinite
• D. 0

Answer 1

The correct option is D

0

Given equation $e^{sinx}-e^{-sinx}-4=0$

Let $e^{sinx}=y$, then given equation can be written as

$y^2-4y-1=0$ ⇒ $y=2\pm \sqrt{5}$

But the value of $y=e^{sinx}$ is always positive, so

$y=2+\sqrt{5}$ (∵ 2 < $\sqrt{5}$

⇒$lo{g}_{e}y=lo{g}_e(2+\sqrt{5})$ ⇒ sin x = $lo{g}_e(2+\sqrt{5})>1$

no solution