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

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

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

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

x = 2 πn, x = π + 2 πn

Solution steps

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

Subtract

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

from both sides

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

Factor

sin^{3} (x) - sin^{3} (x) cos (x) : - sin^{3} (x) (cos (x) - 1)

- sin^{3} (x) (cos (x) - 1) = 0

Solving each part separately

sin^{3} (x) = 0 or cos (x) - 1 = 0

sin^{3} (x) = 0 : x = 2 πn, x = π + 2 πn

cos (x) - 1 = 0 : x = 2 πn

Combine all the solutions

x = 2 πn, x = π + 2 πn

sec^{2} (x) - 1 = tan (x)

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

2 sin (2 x) = cos (x)

(tan (θ) + 1) (sec (θ) - 2) = 0

sin (3 x) = 2 sin (x)

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