Find all solutions of the equation in the interval 0 2 pi 2

Find all solutions of the equation in the interval [0, 2 pi]. 2 cos 4x cos 2x + 2 sin 4x sin 2x = Squareroot 2 Write your answer in radians in terms of pi. If there is more than one solution, separate them with comment.

Solution

2cos4xcos2x + 2sin4x sin2x = sqrt2

Divide by 2 the whole equation:

cos4xcos2x + sin4x sin2x = sqrt2/2

Us ethe formula : cos(a-b) = cosacosb +sinasinb

So, cos(4x -2x) = sqrt(2)/2

cos2x = sqrt(2)/2

x = pi/8

x = 7pi/8

x= 15pi/8

x= 9pi/8

Solution x= pi/8, 7pi/8, 15pi/8, 9pi/8