Algebra Examples

$\tan^{2} (θ) \cdot \cot^{2} (θ)$

Step 1

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

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

Step 2

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

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

Step 3

Apply basic rules of exponents.

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Step 3.1

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

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

Step 3.2

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

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

Step 4

Cancel the common factor of $\sin^{2} (θ)$ .

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Step 4.1

Cancel the common factor.

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

Step 4.2

Rewrite the expression.

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

Step 5

Cancel the common factor of $\cos^{2} (θ)$ .

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Step 5.1

Cancel the common factor.

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

Step 5.2

Rewrite the expression.

$1$