## Trigonometry (11th Edition) Clone

$sec~x = \pm \frac{\sqrt{1 - sin^2~x}}{1 - sin^2~x}$
We can find an expression for $cos~x$ in terms of $sin~x$: $sin^2~x+cos^2~x = 1$ $cos^2~x = 1 - sin^2~x$ $cos~x = \pm~\sqrt{1 - sin^2~x}$ We can write $sec~x$ in terms of $sin~x$: $sec~x = \frac{1}{cos~x}$ $sec~x = \frac{1}{\pm~\sqrt{1 - sin^2~x}}$ $sec~x = \frac{1}{\pm~\sqrt{1 - sin^2~x}}~\frac{\sqrt{1 - sin^2~x}}{\sqrt{1 - sin^2~x}}$ $sec~x = \pm \frac{\sqrt{1 - sin^2~x}}{1 - sin^2~x}$