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