What is the general solution for -2sin^2(x)-sin(x)+3=0 ?

The general solution for -2sin^2(x)-sin(x)+3=0 is x= pi/2+2pin

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-2sin^2(x)-sin(x)+3=0

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

x = \frac{π}{2} + 2 πn

Solution steps

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

Solve by substitution

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

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

No Solution

sin (x) = 1 : x = \frac{π}{2} + 2 πn

Combine all the solutions

x = \frac{π}{2} + 2 πn

tan (x) = - 3 + 2

3 tan (x) - cot (x) = 0

sin^{2} (x) = \frac{( 2 m - 1 )}{4}

cos (2 x) - 0.25 = 0

2 tan^{2} (x) + 1 = cos (x)

What is the general solution for -2sin^2(x)-sin(x)+3=0 ?
The general solution for -2sin^2(x)-sin(x)+3=0 is x= pi/2+2pin