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

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

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

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

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

Solution steps

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

Solve by substitution

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

sin (x) = 0 : x = 2 πn, x = π + 2 πn

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

sin (x) = 1 : x = \frac{π}{2} + 2 πn

Combine all the solutions

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

\frac{2 cos ( θ )}{tan ( θ )} = cot (θ)

sin^{4} (x) = 0

tan (θ) = \frac{7}{24}

- 22 = - 2 sec (x + 15 0^{\circ})

9 sin (θ) + 11 = 0

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