What is the general solution for 4-2sin^2(x)=-sin(x)+3 ?

The general solution for 4-2sin^2(x)=-sin(x)+3 is x=(7pi)/6+2pin,x=(11pi)/6+2pin,x= pi/2+2pin

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4-2sin^2(x)=-sin(x)+3

4 - 2 sin^{2} (x) = - sin (x) + 3

x = \frac{7 π}{6} + 2 πn, x = \frac{11 π}{6} + 2 πn, x = \frac{π}{2} + 2 πn

Solution steps

4 - 2 sin^{2} (x) = - sin (x) + 3

Solve by substitution

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

sin (x) = - \frac{1}{2} : x = \frac{7 π}{6} + 2 πn, x = \frac{11 π}{6} + 2 πn

sin (x) = 1 : x = \frac{π}{2} + 2 πn

Combine all the solutions

x = \frac{7 π}{6} + 2 πn, x = \frac{11 π}{6} + 2 πn, x = \frac{π}{2} + 2 πn

csc^{3} (x) + csc^{2} (x) = 2 csc (x) + 2

cot^{2} (x) sin (x) = cot^{2} (x)

2 cos^{2} (w) + cos (w) - 3 = 0

csc (2 x) = \frac{3}{2}

sin (\frac{θ}{4}) = \frac{1}{2}

What is the general solution for 4-2sin^2(x)=-sin(x)+3 ?
The general solution for 4-2sin^2(x)=-sin(x)+3 is x=(7pi)/6+2pin,x=(11pi)/6+2pin,x= pi/2+2pin