Trigonometry Examples

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

Step 1

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

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

Step 2

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

$\frac{(\csc (x) + 1) (\csc (x) - 1)}{1 + \csc (x)}$