Simplify (sec(x)^2)/(cot(x)^2+1)

$\frac{\sec^{2} (x)}{\cot^{2} (x) + 1}$

Rearrange terms.

$\frac{\sec^{2} (x)}{1 + \cot^{2} (x)}$

Apply pythagorean identity.

$\frac{\sec^{2} (x)}{\csc^{2} (x)}$

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

${(\frac{\sec (x)}{\csc (x)})}^{2}$

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

${(\frac{\sec (x)}{\frac{1}{\sin (x)}})}^{2}$

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

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

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

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

Convert from $\frac{\sin (x)}{\cos (x)}$ to $\tan (x)$ .

$\tan^{2} (x)$