Linearize the Trigonometric Powers Part 1

Geometry Level 1

$\cos^2 \theta = a_2 \cos (2 \theta) + a_0$

Above shows a trigonometric identity for constants $a_0, a_2$ .

What is the value of $a_0 + a_2$ ?

1 solution

Jake Lai
May 6, 2015

We rearrange the identity $\cos 2\theta = 2\cos^{2} \theta -1$ as

$\cos^{2} \theta = \frac{1}{2} \cos 2\theta + \frac{1}{2}$

It can be seen that $a_{0} = a_{2} = \frac{1}{2}$ . Hence, $a_{0}+a_{2} = \boxed{1}$ .