Trigonometry Examples

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

Step 1

Simplify the denominator.

Tap for more steps...

Step 1.1

Factor $\cos (x)$ out of $\cos (x) - \cos (x) \sin (x)$ .

Tap for more steps...

Step 1.1.1

Multiply by $1$ .

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

Step 1.1.2

Factor $\cos (x)$ out of $- \cos (x) \sin (x)$ .

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

Step 1.1.3

Factor $\cos (x)$ out of $\cos (x) \cdot 1 + \cos (x) (- 1 \sin (x))$ .

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

Step 1.2

Rewrite $- 1 \sin (x)$ as $- \sin (x)$ .

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

Step 2

Cancel the common factor of $\cos^{2} (x)$ and $\cos (x)$ .

Tap for more steps...

Step 2.1

Factor $\cos (x)$ out of $\cos^{2} (x)$ .

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

Step 2.2

Cancel the common factors.

Tap for more steps...

Step 2.2.1

Cancel the common factor.

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

Step 2.2.2

Rewrite the expression.

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