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

The general solution for -2sin^2(x)=-sin(x)-1 is x=(7pi)/6+2pin,x=(11pi)/6+2pin,x= pi/2+2pin

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

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

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

Solution steps

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

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

tan (x) = \frac{5}{7}

6 sin (2 t) + 9 sin (t) = 0

sin (2 x + 60) + sin (x + 30) = 0

sin (2 x) - 3 cos (2 x) = 0

3 sin (2 x) = 3 cos (x)

What is the general solution for -2sin^2(x)=-sin(x)-1 ?
The general solution for -2sin^2(x)=-sin(x)-1 is x=(7pi)/6+2pin,x=(11pi)/6+2pin,x= pi/2+2pin