Number of solutions of the equation
$2^{x} + x = 2^{sin x} + sin x$ in $[0, 10 π]$ is

5

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6

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11

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1

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Solution

The correct option is D $1$
We know that,
$x \geq sin x \Rightarrow 2^{x} \geq 2^{sin x}$
$∴ x + 2^{x} \geq sin x + 2^{sin x}$
The possible solution when they both are equal will be at $x = 0$

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