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

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

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

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

x = 2 πn, x = π + 2 πn, x = \frac{3 π}{2} + 2 πn

Solution steps

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

Solve by substitution

sin (x) = 0, sin (x) = - 1

sin (x) = 0 : x = 2 πn, x = π + 2 πn

sin (x) = - 1 : x = \frac{3 π}{2} + 2 πn

Combine all the solutions

x = 2 πn, x = π + 2 πn, x = \frac{3 π}{2} + 2 πn

2 sin^{2} (x) - sin (x) - 1 = 0, 0 \leq x < 2 π

sin^{2} (x) = 3

2 cos (2 θ) - 2 = - 3 sin (θ)

cos^{2} (x) = cos (2 x)

sin (\frac{π}{6} + x) + sin (\frac{π}{6} - x) = \frac{1}{2}

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