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

$\frac{\csc^{2} (θ)}{\sec^{2} (θ)}$

Step 1

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

${(\frac{\csc (θ)}{\sec (θ)})}^{2}$

Step 2

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

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

Step 3

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

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

Step 4

Multiply by the reciprocal of the fraction to divide by $\frac{1}{\cos (θ)}$ .

${(\frac{\cos (θ)}{\sin (θ)})}^{2}$

Step 5

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

$\cot^{2} (θ)$