+13 Problem:
Find the 3 smallest positive x-intercepts of the graph of
\[y = \cos(12x) + \cos(16x)\]
and list them in increasing order.
Enter your answer as a list of x-coordinates from least to greatest.
Use the identity
\(\displaystyle \cos A + \cos B = 2\cos\left(\frac{A+B}{2}\right)\cos \left( \frac{A-B}{2}\right).\)
Then,
\(\displaystyle \cos(12x)+\cos(16x)=2\cos(14x)\cos(2x)\\ =0\\ \text{ when } \\ 14x = \pi/2 + m\pi \\ \text{or when } \\ 2x = \pi/2 +n\pi, \ \text{ m and n integers.}\)
Smallest will be when m = 0, then x = pi/28, etc.
