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If

Question:

If $\frac{\pi}{2}

Solution:

$\because \frac{\pi}{2}

$\therefore \sqrt{\frac{1+\cos 2 x}{2}}=\sqrt{\frac{2 \cos ^{2} x}{2}}=|\cos x|$

In second quadrant $\cos x$ is negative.

$\therefore \sqrt{\frac{1+\cos 2 x}{2}}=-\cos x$

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