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

The general solution for sin(x)+2sin^2(x)=0 is x=2pin,x=pi+2pin,x=(7pi)/6+2pin,x=(11pi)/6+2pin

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

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

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

Solution steps

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

Solve by substitution

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

sin (x) = 0 : x = 2 πn, x = π + 2 πn

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

Combine all the solutions

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

5 sec^{2} (x) - 5 = 0, 0 \leq x \leq 2 π

4 cos^{2} (θ) + 4 = 5

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0.34 = cos (x)

7 sin (x) cos (x) + cos^{2} (x) = 1

What is the general solution for sin(x)+2sin^2(x)=0 ?
The general solution for sin(x)+2sin^2(x)=0 is x=2pin,x=pi+2pin,x=(7pi)/6+2pin,x=(11pi)/6+2pin