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

The general solution for sin^3(x)=sin^3(x)tan(x) is x=2pin,x=pi+2pin,x= pi/4+pin

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

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

x = 2 πn, x = π + 2 πn, x = \frac{π}{4} + πn

Solution steps

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

Subtract

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

from both sides

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

Factor

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

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

Solving each part separately

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

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

tan (x) - 1 = 0 : x = \frac{π}{4} + πn

Combine all the solutions

x = 2 πn, x = π + 2 πn, x = \frac{π}{4} + πn

- 4 sin^{2} (θ) - 7 sin (θ) + 7 = 0

2 cos^{2} (4 x) = 1

sin (2 x) cos (x) + cos (2 x) sin (x) = \frac{1}{2}

csc^{2} (x) + 3 csc (x) + 2 = 0

2 sin (x) cos (x) + 2 cos (x) = 0

What is the general solution for sin^3(x)=sin^3(x)tan(x) ?
The general solution for sin^3(x)=sin^3(x)tan(x) is x=2pin,x=pi+2pin,x= pi/4+pin