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If

Question:

If $\frac{\pi}{4}

Solution:

We have,

$\sqrt{1-\sin 2 x}$

$=\sqrt{\sin ^{2} x+\cos ^{2} x-2 \sin x \cos x}$

$=\sqrt{(\sin x-\cos x)^{2}}$

$=|\sin x-\cos x|$

$=\sin x-\cos x$

$\left[\because \sin x>\cos x\right.$ for $\left.\frac{\pi}{4}

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

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