Question

Find all solutions to the equation secx(2cosx-sqrt2)=0

Answer 1

Answer:

Option A.

$x = \frac{\pi}{4} +2k\pi$ and $x = 7\frac{\pi}{4} +2k\pi$

Step-by-step explanation:

We have the following expression:

$secx(2cosx -\sqrt{2}) = 0$

For this equation to fulfill any of the two terms, or both, they must be zero:

That is to say:

$secx = 0$  or  $(2cosx -\sqrt{2}) = 0$

We know that $secx = \frac{1}{cosx}$ is different from 0 for all x.

Then we only have one option left.

$(2cosx -\sqrt{2}) = 0$

We clear x from the equation:

$2cosx = \sqrt{2}$

$cosx = \frac{\sqrt{2}}{2}$

$x = acos(\frac{\sqrt{2}}{2})$

$x = \frac{\pi}{4} +2k\pi$ and $x = 7\frac{\pi}{4} +2k\pi$

where k is an integer