The number of real solutions of the equation ? 1 + cos 2 x ? = 2 cos - 1 ( cos x ) in [ 2 , ] is

Question

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

Smart Achievers · Accepted Answer

(1)

Given, $\sqrt{1 + \cos 2 x} = \sqrt{2} \cos^{- 1} (\cos x)$

$∴$ $\sqrt{2}$ $| \cos x |$ $= \sqrt{2} x$

For all $x \in [\frac{π}{2}, π],$ $- \cos x = x$

$\Rightarrow No Solution$

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