One root of the equation $2 cos x + 1 = 2 x$ lies in the interval

[- \frac{π}{2}, 0]

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[0, \frac{π}{2}]

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[\frac{π}{2}, π]

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none of these

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Solution

The correct option is B $[0, \frac{π}{2}]$
Let take $f (x) = 2 cos x + 1 - 2 x$
If given interval is $(a, b)$ and if root is lies in this interval than $f (a) f (b) < 0$
checking this for all options, then
we will get $f (0) f (\frac{π}{2}) < 0$

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