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 sin^2x + 3 cos x = 3 Write your answer in radians in terms of pi. If there is more than one solution, separate them with commas. X =

Solution

2sin^2 x + 3 cos x=3

sin^2=1-cos^2 x

2(1-cos^2 x) + 3cos x=3

2-2cos^2 x +3cosx-3=0

-2cos^2x +3cos x-1=0

2cos^2 x -3cos x +1=0

(2cos x-1)(cos x-1)=0

cos x=1/2 and cos x=1

x= pi/3,5pi/3 and 0