Question

What are all the exact solutions of square root 2 cosx-1=0 for 0 less than or equal to x less than or equal to 2 pi ?Give your answer in radians.

Answer 1

Answer: $x=\frac{\pi}{4}\ or\ \frac{7\pi}{4}$

Step-by-step explanation:

Given equation is

$\sqrt{2}\cos x-1=0$

solving this

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

There can be two solution because $0$

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

so, $x=\frac{\pi}{4}\ or\ \frac{7\pi}{4}$