Question

State the whether given equation is true or false

Prove that:$\cos (\frac{\pi }{4}+x)+\cos (\frac{\pi }{4}-x)=\sqrt{2}\cos x$

• A. True
• B. False

Answer 1

The correct option is A True

Prove that

$\cos (\frac{\pi }{4}+x)+\cos (\frac{\pi }{4}-x)=\sqrt{2}\cos x$

Apply $\cos (A+B)=\cos A\cos B-\sin A\sin B$ and

$\cos (A-B)=\cos A\cos B+\sin A\sin B$ in LHS

LHS.

$=\cos \frac{\pi }{4}\cos c-\sin \frac{\pi }{4}\sin x+\cos \frac{\pi }{4}\cos x+\sin \frac{\pi }{4}\sin x$

$=2\cos \frac{\pi }{4}\cos x$

$=2\times \frac{1}{\sqrt{2}}\cos x$

$=\sqrt{2}\cos x$