Question

find all the solutions to secx=sqrt2

Answer 1

secx=sqrt2
secx=1/cosx
1/cosx=sqrt2
1/sqrt2=cosx
at x= 45or pi/4 cos give this value

Answer 2

"find all the solutions"

So \(\pi/4\) is not only solution here.

In range \([-\pi,\pi)\), \(\cos x = \dfrac{1}{\sqrt2}\) is true at \(x=\pi/4\) and \(\)\(-\pi/4\)

So all solutions are \(x = \dfrac{\pi}{4}+2\pi~n,~ n\in\mathbb{Z}\) and \( -\dfrac{\pi}{4}+2\pi~n,~ n\in\mathbb{Z}\)

Answer 3

that is understandable