Question

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

• A. $1$
• B. $2$
• C. Infinite
• D. None

Answer 1

The correct option is A $1$

$e^{\sin x}-e^{-\sin x}-4=0$

Taking log on both the sides, we get :

$\sin x-(-\sin x)-\log 4=0$

$2\sin x-0.602=0$

$2\sin x=0.602$

$\sin x=\frac{0.602}{2}=0.301$

$x\in [-1,1]$

$\therefore$ Real roots $=1$