Precalculus Examples

$\frac{2 \tan (\frac{2 π}{5})}{1 - \tan^{2} (\frac{2 π}{5})}$

Step 1

Rewrite $1$ as $1^{2}$ .

$\frac{2 \tan (\frac{2 π}{5})}{1^{2} - \tan^{2} (\frac{2 π}{5})}$

Step 2

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = 1$ and $b = \tan (\frac{2 π}{5})$ .

$\frac{2 \tan (\frac{2 π}{5})}{(1 + \tan (\frac{2 π}{5})) (1 - \tan (\frac{2 π}{5}))}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$\frac{2 \tan (\frac{2 π}{5})}{(1 + \tan (\frac{2 π}{5})) (1 - \tan (\frac{2 π}{5}))}$

Decimal Form:

$- 0.72654252 \dots$