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

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

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

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

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

Solution steps

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

3 cos (θ) = sin (θ)

csc (θ) = \frac{4}{3}

9^{s i n (x) - 1} + 3 = 3^{s i n (x)} + 3^{s i n (x) - 1}

3 + 3 sin (θ) = 9 sin (θ)

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

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