stuck on this trig problem Please help Solve the trigonometr

stuck on this trig problem

Please help

Solve the trigonometric equation 2sin^4 x - 3sin^2 x + 1 = 0 in the interval [0,2pi).

Solution

let us subsitute sin²x= t

2sin⁴x- 3sin²x +1=0

2t²-3t +1=0

2t²-2t-t +1=0

2t(t-1) -1(t-1)=0

(2t-1)(t-1)=0

t =1/2 ,t=1

sin²x= 1/2 , sin²x= 1

sinx =-1/2 ,sinx= 1/2 ,sinx=-1,sinx=1

sinx =-1/2

x=5/4,7/4,

sinx =1/2

=>x=/4 ,3/4 ,

sinx =-1

=>x=3/2

sinx =1

=>x=/2