First slide

Trigonometric equations

Question

$No. of solutions of \sin x = e^{x} + e^{- x}$

Easy

A

2
B

0
C

3
D

4

Solution

We have
$\begin{array}{l} \frac{e^{x} + e^{- x}}{2} \geq \sqrt{e^{x} e^{- x}} (∵ A m, > G m) \\ \Rightarrow e^{x} + e^{- x} \geq 2 \\ \Rightarrow \sin x \geq 2 \end{array}$
$\Rightarrow t h e g i v e n e q u a t i o n h a s n o s o l u t i o n (∵ - 1 \leq \sin x \leq 1)$

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