Simplify (tan(A)^2+1)/(sec(A))

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

Apply pythagorean identity.

$\frac{\sec^{2} (A)}{\sec (A)}$

Cancel the common factor of $\sec^{2} (A)$ and $\sec (A)$ .

Factor $\sec (A)$ out of $\sec^{2} (A)$ .

$\frac{\sec (A) \sec (A)}{\sec (A)}$

Cancel the common factors.

Multiply by $1$ .

$\frac{\sec (A) \sec (A)}{\sec (A) \cdot 1}$

Cancel the common factor.

$\frac{\sec (A) \sec (A)}{\sec (A) \cdot 1}$

Rewrite the expression.

$\frac{\sec (A)}{1}$

Divide $\sec (A)$ by $1$ .

$\sec (A)$