Trigonometry Examples

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

Step 1

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

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

Step 2

Rewrite $(\cos (x) - \sin (x)) (\cos (x) - \sin (x))$ as ${(\cos (x) - \sin (x))}^{2}$ .

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

Step 3

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 $b = \cos (x) - \sin (x)$ .

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

Step 4

Simplify.

Tap for more steps...

Step 4.1

Apply the distributive property.

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

Step 4.2

Multiply $- - \sin (x)$ .

Tap for more steps...

Step 4.2.1

Multiply $- 1$ by $- 1$ .

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

Step 4.2.2

Multiply $\sin (x)$ by $1$ .

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