Precalculus Examples

$\frac{(\tan (x) + 1) (\tan (x) + 1) - \sec^{2} (x)}{\tan (x)}$

Step 1

Raise $\tan (x) + 1$ to the power of $1$ .

$\frac{{(\tan (x) + 1)}^{1} (\tan (x) + 1) - \sec^{2} (x)}{\tan (x)}$

Step 2

Raise $\tan (x) + 1$ to the power of $1$ .

$\frac{{(\tan (x) + 1)}^{1} {(\tan (x) + 1)}^{1} - \sec^{2} (x)}{\tan (x)}$

Step 3

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{{(\tan (x) + 1)}^{1 + 1} - \sec^{2} (x)}{\tan (x)}$

Step 4

Add $1$ and $1$ .

$\frac{{(\tan (x) + 1)}^{2} - \sec^{2} (x)}{\tan (x)}$

Step 5

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = \tan (x) + 1$ and $b = \sec (x)$ .

$\frac{(\tan (x) + 1 + \sec (x)) (\tan (x) + 1 - \sec (x))}{\tan (x)}$