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

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

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tan^3(x)=tan(x)

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

x = πn, x = \frac{3 π}{4} + πn, x = \frac{π}{4} + πn

Solution steps

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

Solve by substitution

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

tan (x) = 0 : x = πn

tan (x) = - 1 : x = \frac{3 π}{4} + πn

tan (x) = 1 : x = \frac{π}{4} + πn

Combine all the solutions

x = πn, x = \frac{3 π}{4} + πn, x = \frac{π}{4} + πn

3 - 2 sin (x) = 0

- 9 cos^{2} (θ) + 14 sin (θ) + 14 = 0

cos (x) tan (x) = - 7 tan (x)

12 sin^{2} (θ) - 9 = 0

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

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