Find at solutions of the equation in the interval 02pi list

Find at solutions of the equation in the interval (0,2pi) list the solutions in order. if there is no solution enter no solution. sin^2=8=4 cos x x=pi/2 x=3pi/2 x=2pi/3 x=4x/3

Solution

given 8sin²x=8-4cosx

8(1-cos²x)=8-4cosx

8-8cos²x=8-4cosx

-8cos²x=-4cosx

2cos²x=cosx

2cos²x-cosx=0

cosx(2cosx -1)=0

cosx=0 , cosx =1/2

x=pi/2,x=3pi/2 , x=pi/3, x=5pi/3

x=pi/3

x=pi/2

x=3pi/2

x=5pi/3