Trigonometry Examples

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

Step 1

Separate fractions.

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

Step 2

Convert from $\frac{1}{\cos (x)}$ to $\sec (x)$ .

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

Step 3

Divide $\frac{\cos (x)}{\sin (x)}$ by $1$ .

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

Step 4

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

$\cot (x) \sec (x)$

Step 5

Rewrite in terms of sines and cosines, then cancel the common factors.

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Step 5.1

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

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

Step 5.2

Cancel the common factors.

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

Step 6

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

$\csc (x)$