Simplify (cot(theta)^2)/(cos(theta)^2)

$\frac{\cot^{2} (θ)}{\cos^{2} (θ)}$

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

${(\frac{\cot (θ)}{\cos (θ)})}^{2}$

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

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

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

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

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

Cancel the common factor.

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

Rewrite the expression.

${(\frac{1}{\sin (θ)})}^{2}$

Simplify the expression.

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

$\frac{1^{2}}{\sin^{2} (θ)}$

One to any power is one.

$\frac{1}{\sin^{2} (θ)}$

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

$\frac{1^{2}}{\sin^{2} (θ)}$

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

${(\frac{1}{\sin (θ)})}^{2}$

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

$\csc^{2} (θ)$