Answer:
Option 2 - [tex]x=\frac{\pi}{4},\frac{7\pi}{4}[/tex]
Step-by-step explanation:
Given : Expression [tex]\sqrt{2}\cos x-1=0[/tex] for [tex]0\leq x\leq 2\pi[/tex]
To find : What are all the exact solutions of expression?
Solution :
First we simplify the expression,
[tex]\sqrt{2}\cos x-1=0[/tex]
[tex]\sqrt{2}\cos x=1[/tex]
[tex]\cos x=\frac{1}{\sqrt{2}}[/tex]
The general solution is
[tex]x=\frac{\pi}{4}+2\pi n,\frac{7\pi}{4}+2\pi n[/tex]
For [tex]0\leq x\leq 2\pi[/tex]
The solution is [tex]x=\frac{\pi}{4},\frac{7\pi}{4}[/tex]
Therefore, Option 2 is correct.
