Q55 / 160 · WBJEE 2015 · Mathematics

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

  • A
    1
  • B
    2
  • Correct answer
    C
    3
  • D
    4

Solution

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.

Hence, the correct answer is option: 'C'.

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