What is the general solution for 2sin^2(x)-3sin(x)=-1 ?

The general solution for 2sin^2(x)-3sin(x)=-1 is x= pi/2+2pin,x= pi/6+2pin,x=(5pi)/6+2pin

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2sin^2(x)-3sin(x)=-1

2 sin^{2} (x) - 3 sin (x) = - 1

x = \frac{π}{2} + 2 πn, x = \frac{π}{6} + 2 πn, x = \frac{5 π}{6} + 2 πn

Solution steps

2 sin^{2} (x) - 3 sin (x) = - 1

Solve by substitution

sin (x) = 1, sin (x) = \frac{1}{2}

sin (x) = 1 : x = \frac{π}{2} + 2 πn

sin (x) = \frac{1}{2} : x = \frac{π}{6} + 2 πn, x = \frac{5 π}{6} + 2 πn

Combine all the solutions

x = \frac{π}{2} + 2 πn, x = \frac{π}{6} + 2 πn, x = \frac{5 π}{6} + 2 πn

3 cos^{2} (θ) + 2 sin (θ) - 1 = 0

2 sin^{2} (θ) - 3 sin (θ) - 2 = 0

2 cos (x) - 1 = 0

cos (x) = cos (2 x)

0 = sin (x)

What is the general solution for 2sin^2(x)-3sin(x)=-1 ?
The general solution for 2sin^2(x)-3sin(x)=-1 is x= pi/2+2pin,x= pi/6+2pin,x=(5pi)/6+2pin