Question

principal root of this equation: $2cos(x) = \sqrt{2}$

Answer 1

Let's solve the equation:

$\begin{gathered} 2\cos x=\sqrt[]{2} \\ \cos x=\frac{\sqrt[]{2}}{2} \\ x=\cos ^{-1}(\frac{\sqrt[]{2}}{2}) \\ x=\frac{\pi}{4} \end{gathered}$

Therefore the principal root is:

$\frac{\pi}{4}$