Chapter 13.8, Problem 15WE

To determine

To find: The exact value of the given function.

Answer to Problem 15WE

The exact value of the given function is $\frac{\sqrt{3}}{2}$ .

Explanation of Solution

Given information:

The function is ${\cos }^2\frac{\pi }{12}-{\sin }^2\frac{\pi }{12}$ .

Calculation:

Consider the function,

  $\begin{array}{c}{\cos }^2\frac{\pi }{12}-{\sin }^2\frac{\pi }{12}=\cos 2\left(\frac{\pi }{12}\right)\\ =\cos \frac{\pi }{6}\\ =\frac{\sqrt{3}}{2}\end{array}$