Answer:
Option A.
[tex]x = \frac{\pi}{4} +2k\pi[/tex] and [tex]x = 7\frac{\pi}{4} +2k\pi[/tex]
Step-by-step explanation:
We have the following expression:
[tex]secx(2cosx -\sqrt{2}) = 0[/tex]
For this equation to fulfill any of the two terms, or both, they must be zero:
That is to say:
[tex]secx = 0[/tex] or [tex](2cosx -\sqrt{2}) = 0[/tex]
We know that [tex]secx = \frac{1}{cosx}[/tex] is different from 0 for all x.
Then we only have one option left.
[tex](2cosx -\sqrt{2}) = 0[/tex]
We clear x from the equation:
[tex]2cosx = \sqrt{2}[/tex]
[tex]cosx = \frac{\sqrt{2}}{2}[/tex]
[tex]x = acos(\frac{\sqrt{2}}{2})[/tex]
[tex]x = \frac{\pi}{4} +2k\pi[/tex] and [tex]x = 7\frac{\pi}{4} +2k\pi[/tex]
where k is an integer
