Question

If \(e^{\sin x}-e^{-\sin x}-4=0\), then the number of real values of \(x\) is
(A) 0
(B) 1
(C) 2
(D) 3

Answer 1

Ans: (A)
Hint \(: e^{\sin x}-\frac{1}{e^{\sin x}}-4=0\)
\(\Rightarrow \mathrm{e}^{\sin x}=2 \pm \sqrt{5}\)
\(\because-1 \leq \sin x \leq 1\)
\(\Rightarrow \frac{1}{e} \leq e^{\sin x} \leq e\)
\(\Rightarrow\) No solutions exist