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

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

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sin^3(x)=sin(x),0<= x<= 2pi

sin^{3} (x) = sin (x), 0 \leq x \leq 2 π

x = 0, x = π, x = 2 π, x = \frac{3 π}{2}, x = \frac{π}{2}

Solution steps

sin^{3} (x) = sin (x), 0 \leq x \leq 2 π

Solve by substitution

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

sin (x) = 0, 0 \leq x \leq 2 π : x = 0, x = π, x = 2 π

sin (x) = - 1, 0 \leq x \leq 2 π : x = \frac{3 π}{2}

sin (x) = 1, 0 \leq x \leq 2 π : x = \frac{π}{2}

Combine all the solutions

x = 0, x = π, x = 2 π, x = \frac{3 π}{2}, x = \frac{π}{2}

x, 1 + cos (x) = 3 cos (x)

\frac{1}{cos ( x )} = 4

sin (θ) = - 0.15

2 cos (4 x) = 1

cos (2 x) = 2 sin (2 x)

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