Algebra Examples

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

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 $b = \sin (x)$ .

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

Step 2

Cancel the common factor of $\cos (x) - \sin (x)$ .

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Step 2.1

Cancel the common factor.

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

Step 2.2

Divide $\cos (x) + \sin (x)$ by $1$ .

$\cos (x) + \sin (x)$