Precalculus Examples

$\sec^{3} (x) \cot^{3} (x)$

Step 1

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

${(\frac{1}{\cos (x)})}^{3} \cot^{3} (x)$

Step 2

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

${(\frac{1}{\cos (x)})}^{3} {(\frac{\cos (x)}{\sin (x)})}^{3}$

Step 3

Simplify the expression.

Tap for more steps...

Step 3.1

Apply the product rule to $\frac{1}{\cos (x)}$ .

$\frac{1^{3}}{\cos^{3} (x)} {(\frac{\cos (x)}{\sin (x)})}^{3}$

Step 3.2

Apply the product rule to $\frac{\cos (x)}{\sin (x)}$ .

$\frac{1^{3}}{\cos^{3} (x)} \cdot \frac{\cos^{3} (x)}{\sin^{3} (x)}$

Step 3.3

One to any power is one.

$\frac{1}{\cos^{3} (x)} \cdot \frac{\cos^{3} (x)}{\sin^{3} (x)}$

Step 4

Multiply $\frac{1}{\cos^{3} (x)}$ by $\frac{\cos^{3} (x)}{\sin^{3} (x)}$ .

$\frac{\cos^{3} (x)}{\cos^{3} (x) \sin^{3} (x)}$

Step 5

Cancel the common factor of $\cos^{3} (x)$ .

Tap for more steps...

Step 5.1

Cancel the common factor.

$\frac{\cos^{3} (x)}{\cos^{3} (x) \sin^{3} (x)}$

Step 5.2

Rewrite the expression.

$\frac{1}{\sin^{3} (x)}$