Algebra Examples

$\tan^{2} (x) \csc (x)$

Step 1

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

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

Step 2

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

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

Step 3

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

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

Step 4

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

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Step 4.1

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

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

Step 4.2

Cancel the common factor.

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

Step 4.3

Rewrite the expression.

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

Step 5

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

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

Step 6

Separate fractions.

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

Step 7

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

$\frac{1}{\cos (x)} \tan (x)$

Step 8

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

$\sec (x) \tan (x)$