Trigonometry Examples

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

Step 1

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

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

Step 2

Combine the numerators over the common denominator.

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

Step 3

Add $1$ and $1$ .

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

Step 4

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

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

Step 5

Move $2$ to the left of $\cos (x)$ .

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

Step 6

Separate fractions.

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

Step 7

Convert from $\frac{\cos (x)}{\sin (x)}$ to $\cot (x)$ .

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

Step 8

Divide $2$ by $1$ .

$2 \cot (x)$