Question

find all the values of x in the interval [o,2pi) that satisfied the equation cos^2(x)=cos^2(x/2)

Answer 1

use identity
\[\cos(2x) = 2\cos^{2} x - 1\]

Answer 2

\[\cos \frac{ x }{ 2 }=\frac{ 1+\cos x }{ 2 }\]