Trigonometry Examples

$\frac{\cot (x) + \cos (x) \csc (x)}{\cos (x)}$

Step 1

Simplify the numerator.

Tap for more steps...

Step 1.1

Rewrite $\cot (x)$ in terms of sines and cosines.

$\frac{\frac{\cos (x)}{\sin (x)} + \cos (x) \csc (x)}{\cos (x)}$

Step 1.2

Rewrite $\csc (x)$ in terms of sines and cosines.

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

Step 1.3

Combine $\cos (x)$ and $\frac{1}{\sin (x)}$ .

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

Step 1.4

Add $\frac{\cos (x)}{\sin (x)}$ and $\frac{\cos (x)}{\sin (x)}$ .

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

Step 2

Combine $2$ and $\frac{\cos (x)}{\sin (x)}$ .

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

Step 3

Multiply the numerator by the reciprocal of the denominator.

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

Step 4

Cancel the common factor of $\cos (x)$ .

Tap for more steps...

Step 4.1

Factor $\cos (x)$ out of $2 \cos (x)$ .

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

Step 4.2

Cancel the common factor.

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

Step 4.3

Rewrite the expression.

$\frac{2}{\sin (x)}$

Step 5

Separate fractions.

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

Step 6

Convert from $\frac{1}{\sin (x)}$ to $\csc (x)$ .

$\frac{2}{1} \csc (x)$

Step 7

Divide $2$ by $1$ .

$2 \csc (x)$