Trigonometry Examples

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

Step 1

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

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

Step 2

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

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

Step 3

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

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

Step 4

Add $1$ and $1$ .

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

Step 5

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

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

Step 6

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

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