Precalculus Examples

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

Step 1

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

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

Step 2

Apply the sine double-angle identity.

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