Chapter 13.6, Problem 12WE

To determine

To find: The simplification for given term.

Answer to Problem 12WE

The simplification is ${\tan }^{2}t$ .

Explanation of Solution

Given:

The given term is,

  $\frac{\sec t}{\cos t}-\sec t\cos t$

Calculation:

The term is simplified as,

  $\begin{array}{c}\frac{\sec t}{\cos t}-\sec t\cos t=\frac{1}{\cos t\times \cos t}-\frac{1}{\cos t}\times \cos t\\ =\frac{1}{{\cos }^{2}t}-1\\ ={\sec }^{2}t-1\\ ={\tan }^{2}t\end{array}$

Therefore, the simplification is ${\tan }^{2}t$ .