What is the general solution for sin(x)+sin^2(x)+sin^3(x)=0 ?

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

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

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

x = 2 πn, x = π + 2 πn

Solution steps

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

Solve by substitution

sin (x) = 0, sin (x) = - \frac{1}{2} + i \frac{3}{2}, sin (x) = - \frac{1}{2} - i \frac{3}{2}

sin (x) = 0 : x = 2 πn, x = π + 2 πn

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

No Solution

sin (x) = - \frac{1}{2} - i \frac{3}{2} :

No Solution

Combine all the solutions

x = 2 πn, x = π + 2 πn

tan (t) = 4

cos (\frac{x}{3}) = sin (x)

1 + 4 \cdot sin (x) = 2

cos (θ) = \frac{7}{8}

sec (x) (2 sin (x) + 1) - 2 (2 sin (x) + 1) = 0

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