Points: 0 of 1
Establish the identity.
\[
1+\frac{\tan ^{2} \theta}{\sec \theta+1}=\sec \theta
\]
Simplify the numerator of the fraction from the left side by applying the appropriate Pythagorean Identity.
\[
1+\frac{\square}{\sec \theta+1} \text { (Do not factor.) }
\]
Answer
Final Answer: The simplified numerator of the fraction from the left side of the equation is \(\boxed{\sec^2\theta - 1}\)
Step 1 ：Establish the identity: \(1+\frac{\tan ^{2} \theta}{\sec \theta+1}=\sec \theta\)
Step 2 ：Simplify the numerator of the fraction from the left side by applying the appropriate Pythagorean Identity: \(1+\frac{\square}{\sec \theta+1}\)
Step 3 ：The Pythagorean Identity for trigonometric functions states that \(\tan^2\theta = \sec^2\theta - 1\). Substitute this into the equation to simplify the numerator of the fraction on the left side.
Step 4 ：Final Answer: The simplified numerator of the fraction from the left side of the equation is \(\boxed{\sec^2\theta - 1}\)
