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

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

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

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

x = 2 πn, x = π + 2 πn

Solution steps

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

Solve by substitution

sin (x) = 0, sin (x) = - 3, sin (x) = 3

sin (x) = 0 : x = 2 πn, x = π + 2 πn

sin (x) = - 3 :

No Solution

sin (x) = 3 :

No Solution

Combine all the solutions

x = 2 πn, x = π + 2 πn

cos^{4} (x) + 2 sin^{2} (x) + 6 cos^{2} (x) + 5 = 0

1 + sin (2 a) = sin^{2} (a)

\frac{( cos ^{3} ( a ) )}{( 2 cos ^{2} ( a ) - 1 )} = cos (a)

cos (x - 4 5^{\circ}) = 0

7 tan^{2} (x) - 15 = 0

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