Question

The value of $\cos (\pi /4+x)+\cos (\pi /4-x)$ is

• A. $\sqrt{2}{\sin }^{2}x$
• B. $\sqrt{2}\sin x$
• C. $\sqrt{2}{\cos }^{2}x$
• D. $\sqrt{3}\cos x$
• E. $\sqrt{2}\cos x$

Answer 1

Answer: (E)

We have, $\cos \left(\frac{\pi }{4}+x\right)+\cos \left(\frac{\pi }{4}-x\right)$
$=\cos \frac{\pi }{4}\cos x-\sin \frac{\pi }{4}\sin x+\cos \frac{\pi }{4}\cos x+\sin \frac{\pi }{4}\sin x$
$=2\cos \frac{\pi }{4}\cos x$
$=2\times \frac{1}{\sqrt{2}}\cos x$
$=\sqrt{2}\cos x$