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

$b = 1$ .

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