The number of real solutions of the equation $(sin x - x) (cos x - x^{2}) = 0$ is

1

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2

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3

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4

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Solution

The correct option is B $3$
Given,
$(sin x - x) (cos x - x^{2}) = 0$
$\Rightarrow sin x = x$ or $cos x = x^{2}$
Now, if $sin x = x$ , then only one solution i.e. $x = 0$ is possible.
Also, if $cos x = x^{2}$ , then two solutions are possible.
Hence, there are total $3$ solutions.

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