Question

If $\frac{\pi }{2}<x<\frac{3\pi }{2}$, then write the value of $\sqrt{\frac{1+\cos 2x}{2}}$.

Answer 1

$$\begin{gathered} \because \frac{\mathrm{\pi }}{2}<x<\frac{3\mathrm{\pi }}{2} \\ \therefore \sqrt{\frac{1+\cos 2x}{2}}=\sqrt{\frac{2{\cos }^{2}x}{2}}=\left|\cos x\right| \\ \mathrm{In}\mathrm{second}\mathrm{quadrant}\cos x\mathrm{is}\mathrm{negative}. \\ \therefore \sqrt{\frac{1+\cos 2x}{2}}=-\cos x \end{gathered}$$