If π/2 less than x less than 3π/2, then write the value of √{(1 + cos 2x)/2}

If π/2 < x < 3π/2, Then Find √[(1 + cos 2x)/2]

If \[ \frac{\pi}{2}

Using the identity

\[ \frac{1+\cos2x}{2}=\cos^2x \]

Therefore,

\[ \sqrt{\frac{1+\cos2x}{2}} = \sqrt{\cos^2x} = |\cos x| \]

Since

\[ \frac{\pi}{2} the angle \(x\) lies in the second or third quadrant, where \(\cos x\) is negative. Hence,

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

Therefore,

\[ \sqrt{\frac{1+\cos2x}{2}} = -\cos x \]

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

Spread the love