Trigonometry Examples

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

Step 1

Raise $\sin (x) - \cos (x)$ to the power of $1$ .

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

Step 2

Raise $\sin (x) - \cos (x)$ to the power of $1$ .

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

Step 3

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

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

Step 4

Add $1$ and $1$ .

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

Step 5

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

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

Step 6

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

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