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The number of real solutions of the equation $(\sin x-x)\left(\cos x-x^{2}\right)=0$ is
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The correct answer is:
3
Given, $(\sin x-x)\left(\cos x-x^{2}\right)=0$
$\Rightarrow \quad \sin x=x$ or $\cos x=x^{2}$
Now, if $\sin x=x,$ then only one solution ie $x=0$ is possible. Also, if $\cos x=x^{2}$, then two solutions are possible. Hence, there are total 3 solutions.
$\Rightarrow \quad \sin x=x$ or $\cos x=x^{2}$
Now, if $\sin x=x,$ then only one solution ie $x=0$ is possible. Also, if $\cos x=x^{2}$, then two solutions are possible. Hence, there are total 3 solutions.
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