Simplify (sin(x)^2+cos(x)^2)/(tan(x)^2+1)

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

Step 1

Apply pythagorean identity.

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

Step 2

Apply pythagorean identity.

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

Step 3

Simplify with factoring out.

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

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

Rewrite $\frac{1^{2}}{\sec^{2} (x)}$ as ${(\frac{1}{\sec (x)})}^{2}$ .

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

Step 4

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

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

Step 5

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

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

Step 6

Multiply $\cos (x)$ by $1$ .

$\cos^{2} (x)$