Question

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

• A. 2
• B. 1
• C. Infinite
• D. None of these

Answer 1

Answer: (D)

None of these

Answer 2

Let e^sinx = y, then

$y - \frac{1}{y} = 4$ ⇒$y = 2 \pm \sqrt{5}$= 4.23, –0.23

y = e^sinx ≠ – 0.23, y = e^{sin x} = 4.23

⇒ sinx = log 4.23 > 1

Which is not possible