Solve the equation in the domain 0 2 pi Show all steps 4 cos

Solve the equation in the domain [0, 2 pi). Show all steps! 4 cos^2 2x-3 = 0 cos^4 x - cos 2x = 0 sin x + 1 = cos x sin(x - pi/3) = - squareroot 2/2

Solution

4cos²2x-3=0

cos²2x=3/4

cos 2x= +-sqrt3/2

taking cos^-1 on both sides

2x= cos^-1sqrt3/2     or 2x= cos^-1(-sqrt3/2)

2x=pi/6, 5pi/6,7pi/6,11pi/6,13pi/6,17pi/6,19pi/6,23pi/6,

x= pi/12, 5pi/12, 7pi/12,11pi/12, 13pi/12,17pi/12,19pi/12,23pi/12