Solve each equation for exact solutions over the interval 0

Solve each equation for exact solutions over the interval [0, 2 pi]. Round approximate solutions to four decimal places: 3sin^2 x - 5 sin x + 2 = 0 sec^2 2x = 2

Solution

a. 3sin²x-5sin x +2=0

3sin²x-3 sin x -2 sin x +2=0

3sin x(sinx -1)-2(sin x-1)=0

(3sinx -2)(sin x -1)=0

sin x=2/3, sin x=1

x= .73, 2.412,pi/2

b. sec² 2x=2

1/cos²2x=2

cos²2x=1/2

cos 2x=+-sqrt(1/2)

x=pi/8, 3pi/8, 5pi/8, 7pi/8,9pi/8,11pi/8,13pi/8,15pi/8