Trigonometry Examples

$\frac{\sin^{8} (a)}{\sin^{2} (a) - \cos^{2} (a)} - \frac{\cos^{8} (a)}{\sin^{2} (a) - \cos^{2} (a)}$

Step 1

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

$\frac{\sin^{8} (a)}{(\sin (a) + \cos (a)) (\sin (a) - \cos (a))} - \frac{\cos^{8} (a)}{\sin^{2} (a) - \cos^{2} (a)}$

Step 2

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

$\frac{\sin^{8} (a)}{(\sin (a) + \cos (a)) (\sin (a) - \cos (a))} - \frac{\cos^{8} (a)}{(\sin (a) + \cos (a)) (\sin (a) - \cos (a))}$