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General Solutions of (sin theta)^2 = (sin alpha)^2 , (cos theta)^2 = (cos alpha)^2 , (tan theta)^2 = (tan alpha)^2

The number of...

Question

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 C $3$
We have $(sin x - x) (cos x - x^{2}) = 0$
$\Rightarrow$ $sin x - x = 0$ or $cos x = x^{2}$

When $sin x - x = 0$

(only one solution)

When $cos x = x^{2}$
(two solutions)
Therefore, the equation has $3$ solutions.

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