Question

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

• A. 1
• B. 2
• C. 3
• D. 4

Answer 1

Answer: (C)

3

Answer 2

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.