# Math Help - Solution of the sec equation

1. ## Solution of the sec equation

Question:
Find the solution of the equation if it is in the first quadrant

$sec^2x-1=0$

Attempt:
$secx=1 ; x= \frac {1}{arccos 1}$
I keep getting infiniate as my answer

Thank you

2. Originally Posted by mj.alawami
Question:
Find the solution of the equation if it is in the first quadrant

$sec^2x-1=0$

Attempt:
$secx=1 ; x= \frac {1}{arccos 1}$
I keep getting infiniate as my answer

Thank you
$\sec^2{x} = 1$

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

$1 = \cos^2{x}$

$\pm 1 = \cos{x}$

If $\cos{x} = -1$ then $x = \{\dots -3\pi, -\pi, \pi, 3\pi, \dots\}$ and if $\cos{x} = 1$ then $x = \{ \dots, -2\pi, 0, 2\pi, \dots \}$.

Therefore $x = n\pi$ where $n$ is an integer.