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

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

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

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

x = 2 πn, x = π + 2 πn

Solution steps

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

Solve by substitution

sin (x) = 0, sin (x) = - 2, sin (x) = 2

sin (x) = 0 : x = 2 πn, x = π + 2 πn

sin (x) = - 2 :

No Solution

sin (x) = 2 :

No Solution

Combine all the solutions

x = 2 πn, x = π + 2 πn

2 cos^{3} (x) = cot^{3} (x)

\frac{1}{( sec ^{2} ( a ) )} + \frac{1}{( cos ^{2} ( a ) )} = 1

(1 - cos (a)) (1 + cos (a)) = tan (a) sin (a)

tan^{2} (x) + \frac{1}{6} + \frac{tan ( 1 )}{3} = 0

- 2 cos^{2} (x) - 5 sin (x) + 5 = 0

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