Chapter 13.6, Problem 44WE

To determine

To simplify: The each expression.

Answer to Problem 44WE

The simplified form of expression is $\csc t$ .

Explanation of Solution

Given:

The given expression is as:

  $\frac{\sec t+\csc t}{1+\tan t}$ .

The simplified form is calculated as:

  $\begin{array}{c}\frac{\sec t+\csc t}{1+\tan t}=\frac{\frac{1}{\cos t}+\frac{1}{\sin t}}{1+\frac{\sin t}{\cos t}}\\ =\frac{\frac{\sin t+\cos t}{\cos t\sin t}}{\frac{\cos t+\sin t}{\cos t}}\\ =\frac{\cos t}{\cos t\sin t}\\ =\frac{1}{\sin t}\end{array}$

Further simplified as:

  $\frac{\sec t+\csc t}{1+\tan t}=\csc t$

Therefore, the simplified form of expression is $\csc t$ .