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

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

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

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

x = \frac{3 π}{2} + 2 πn

Solution steps

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

Solve by substitution

sin (x) = \frac{3}{2}, sin (x) = - 1

sin (x) = \frac{3}{2} :

No Solution

sin (x) = - 1 : x = \frac{3 π}{2} + 2 πn

Combine all the solutions

x = \frac{3 π}{2} + 2 πn

2 sin (x) - csc (x) = 1

2 cos^{2} (x) + 3 cos (x) = 0

2 sin^{3} (x) - sin (x) = 0

(cos (3 θ)) (cos (θ)) - 1 = (sin (3 θ)) (sin (θ))

tan (θ) = - 5

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