Question:
The number of real solutions of the equation $(\sin x-x)\left(\cos x-x^{2}\right)=0$ is
The number of real solutions of the equation $(\sin x-x)\left(\cos x-x^{2}\right)=0$ is
Updated On: Jun 18, 2022
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The Correct Option is C
Solution and Explanation
Given, $(\sin x-x)\left(\cos x-x^{2}\right)=0$
$\Rightarrow \sin x=x$ 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.
$\Rightarrow \sin x=x$ 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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