Trigonometry Examples

$\frac{\csc (x) \cos^{2} (x)}{1 + \csc (x)}$

Step 1

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

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

Step 2

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

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

Step 3

Combine $\frac{1}{\sin (x)}$ and $\cos^{2} (x)$ .

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

Step 4

Multiply the numerator by the reciprocal of the denominator.

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

Step 5

Multiply $\frac{\cos^{2} (x)}{\sin (x)}$ by $\frac{1}{1 + \frac{1}{\sin (x)}}$ .

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

Step 6

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

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

Step 7

Separate fractions.

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

Step 8

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

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

Step 9

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

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

Step 10

Combine $\frac{\cos (x)}{1 + \csc (x)}$ and $\cot (x)$ .

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