Trigonometry Examples

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

Step 1

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

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