First slide

Trigonometric equations

Question

The number of real solutions of the equation $\sin x = 2^{x} + 2^{- x}$ is zero then

Very Easy

A

$|\sin x| \leq 1$
B

$|\sin x| \geq 1$
C

$|\cos x| = 0$
D

$|\cos x| < 1$

Solution

$\begin{array}{l} T h e 2^{x} + 2^{- x} \geq 2 \\ \Rightarrow \sin x \geq 2 w h i c h h a s n o r e a l s o l u t i o n (∵ |\sin x| \leq 1) \end{array}$

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