Solve the equation for all exact solutions 2sin2x 3 sin x

Solve the equation for all exact solutions. 2sin^2x - 3 sin x + 1 = 0

Solution

2sin²x -3sinx +1=0

(2sinx-1)(sinx-1)=1

2sinx-1=0          sinx -1=0

sin x=1/2            sin x=1

x=sin^-1(1/2)             x=sin^-11

x=2pik   + pi/2          x= 2pi k + pi/6 , 2pi k + 5pi/6

x= 2pi k + pi/2, 2pi k + pi/6,2pi k + 5pi/6