Trigonometry Examples

$\sec (2 x)$

Step 1

Expand sec(2x).

$\frac{1}{\cos^{2} (x) - \sin^{2} (x)}$

Step 2

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = \cos (x)$ and $b = \sin (x)$ .

$\frac{1}{(\cos (x) + \sin (x)) (\cos (x) - \sin (x))}$