Algebra Examples

$\tan (θ) \cdot \cot^{2} (θ)$

Step 1

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

$\frac{\sin (θ)}{\cos (θ)} \cdot \cot^{2} (θ)$

Step 2

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

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

Step 3

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

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

Step 4

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

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Step 4.1

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

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

Step 4.2

Cancel the common factor.

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

Step 4.3

Rewrite the expression.

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

Step 5

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

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Step 5.1

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

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

Step 5.2

Cancel the common factor.

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

Step 5.3

Rewrite the expression.

$\frac{\cos (θ)}{\sin (θ)}$

Step 6

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

$\cot (θ)$