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

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

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

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

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

Solution steps

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

Solve by substitution

sin (x) = - \frac{1}{2}, sin (x) = 0

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

sin (x) = 0 : x = 2 πn, x = π + 2 πn

Combine all the solutions

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

sin (2 x) = 0.8

cot (x) = tan (x)

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

3 tan (\frac{x}{2}) - 3 = 0

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

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