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

$\frac{\csc^{2} (θ)}{\cot^{2} (θ)}$

Step 1

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

${(\frac{\csc (θ)}{\cot (θ)})}^{2}$

Step 2

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

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

Step 3

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

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

Step 4

Multiply by the reciprocal of the fraction to divide by $\frac{\cos (θ)}{\sin (θ)}$ .

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

Step 5

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

Cancel the common factor.

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

Rewrite the expression.

${(\frac{1}{\cos (θ)})}^{2}$

Step 6

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

$\sec^{2} (θ)$