The number of solutions of the equation $2 cos x = 2 x^{2} + 1$ in $x \in [- \frac{π}{2}, \frac{π}{2}]$ is

0

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2

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4

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3

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Solution

The correct option is B $2$
$2 cos x = 2 x^{2} + 1 \Rightarrow cos x = x^{2} + \frac{1}{2}$
Now, number of solution of the above equation is equal to the points of intersection of the two curves.
$y = cos x \dots (1)$ and
$y = x^{2} + \frac{1}{2} \dots (2) in [- \frac{π}{2}, \frac{π}{2}]$

From the figure, number of solution is $2$

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