Trigonometry Examples

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

Rewrite $1$ as $1^{2}$ .

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

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = 1$ and $b = \tan (x)$ .

$\frac{2 \tan (x)}{(1 + \tan (x)) (1 - \tan (x))}$