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Trigonometric Equations

The number of...

Question

The number of real solutions of the equation $sin (e^{x}) = 2^{x} + 2^{- x}$ is-

A

1

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B

0

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C

2

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D

Infinite

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Solution

The correct option is B 0
For $sin e^{x} = 2^{x} + 2^{- x}$
$L H S = - 1 \leq sin e^{x} \leq 1 R H S = min (2^{x} + 2^{- x}) = 2$
Hence no solution

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