Trigonometry Examples

$\sec (x) \cot^{2} (x)$

Step 1

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

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

Step 2

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

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

Step 3

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

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

Step 4

Cancel the common factor of $\cos (x)$ .

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Step 4.1

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

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

Step 4.2

Cancel the common factor.

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

Step 4.3

Rewrite the expression.

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

Step 5

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

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

Step 6

Separate fractions.

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

Step 7

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

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

Step 8

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

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