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

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

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

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

x = 2 πn, x = π + 2 πn

Solution steps

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

Solve by substitution

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

sin (x) = 0 : x = 2 πn, x = π + 2 πn

sin (x) = i :

No Solution

sin (x) = - i :

No Solution

Combine all the solutions

x = 2 πn, x = π + 2 πn

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

81 cos^{2} (x) = 16

sec (θ) (sec (θ) - 1) = 2

\frac{sin ( 7 4 ^{\circ} )}{8} = \frac{sin ( x )}{4}

\frac{cos ( x )}{cot ( x )} = sec (x)

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