Question

Determine cos 2x when cos^2x = 2/5, where 0 < x < pi/2.

Answer 1

\(cos (2x) = 2 cos^2 x -1\) so, from yours, \(cos^2x = \dfrac{2}{5}\) time 2 both sides
to get \(2cos^2 x= \dfrac{4}{5}\) and -1 both sides \(2cos^2x -1= \dfrac{4}{5}-1= -\dfrac{1}{5}\) and it is = cos 2x