Precalculus Examples

$\frac{\csc (x) \cot (x)}{\sec (x)}$

Step 1

Separate fractions.

$\frac{\cot (x)}{1} \cdot \frac{\csc (x)}{\sec (x)}$

Step 2

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

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

Step 3

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

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

Step 4

Multiply by the reciprocal of the fraction to divide by $\frac{1}{\cos (x)}$ .

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

Step 5

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

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

Step 6

Divide $\cot (x)$ by $1$ .

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

Step 7

Multiply $\cot (x) \cot (x)$ .

Tap for more steps...

Step 7.1

Raise $\cot (x)$ to the power of $1$ .

$\cot^{1} (x) \cot (x)$

Step 7.2

Raise $\cot (x)$ to the power of $1$ .

$\cot^{1} (x) \cot^{1} (x)$

Step 7.3

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

${\cot (x)}^{1 + 1}$

Step 7.4

Add $1$ and $1$ .

$\cot^{2} (x)$