Algebra Examples

$\frac{\cot^{2} (θ)}{\cos^{2} (θ)}$

Step 1

Rewrite $\frac{\cot^{2} (θ)}{\cos^{2} (θ)}$ as ${(\frac{\cot (θ)}{\cos (θ)})}^{2}$ .

${(\frac{\cot (θ)}{\cos (θ)})}^{2}$

Step 2

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

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

Step 3

Rewrite $\frac{\frac{\cos (θ)}{\sin (θ)}}{\cos (θ)}$ as a product.

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

Step 4

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

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Step 4.1

Cancel the common factor.

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

Step 4.2

Rewrite the expression.

${(\frac{1}{\sin (θ)})}^{2}$

Step 5

Simplify the expression.

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Step 5.1

Apply the product rule to $\frac{1}{\sin (θ)}$ .

$\frac{1^{2}}{\sin^{2} (θ)}$

Step 5.2

One to any power is one.

$\frac{1}{\sin^{2} (θ)}$

Step 5.3

Rewrite $1$ as $1^{2}$ .

$\frac{1^{2}}{\sin^{2} (θ)}$

Step 6

Rewrite $\frac{1^{2}}{\sin^{2} (θ)}$ as ${(\frac{1}{\sin (θ)})}^{2}$ .

${(\frac{1}{\sin (θ)})}^{2}$

Step 7

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

$\csc^{2} (θ)$