Trigonometry Examples

$\frac{\sin^{4} (x) - \cos^{4} (x)}{\cos (x) - \sin (x)}$

Step 1

Rewrite $\sin^{4} (x)$ as ${(\sin^{2} (x))}^{2}$ .

$\frac{{(\sin^{2} (x))}^{2} - \cos^{4} (x)}{\cos (x) - \sin (x)}$

Step 2

Rewrite $\cos^{4} (x)$ as ${(\cos^{2} (x))}^{2}$ .

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

Step 3

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

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

Step 4

Simplify.

Tap for more steps...

Step 4.1

Apply pythagorean identity.

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

Step 4.2

Multiply $\sin^{2} (x) - \cos^{2} (x)$ by $1$ .

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

Step 4.3

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 $b = \cos (x)$ .

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