If π/4 less than x less than π/2, then write the value of √1 - sin 2x.

If π/4 < x < π/2, Then Find the Value of √(1 − sin 2x)

If \[ \frac{\pi}{4}

Using the identity

\[ 1-\sin2x = (\sin x-\cos x)^2 \]

Therefore,

\[ \sqrt{1-\sin2x} = |\sin x-\cos x| \]

Since

\[ \frac{\pi}{4} we have

\[ \sin x>\cos x. \]

Hence,

\[ |\sin x-\cos x| = \sin x-\cos x \]

Therefore,

\[ \sqrt{1-\sin2x} = \sin x-\cos x \]

\[ \boxed{\sin x-\cos x} \]

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