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

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

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tan^3(x)-3tan(x)=0

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

x = πn, x = \frac{2 π}{3} + πn, x = \frac{π}{3} + πn

Solution steps

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

Solve by substitution

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

tan (x) = 0 : x = πn

tan (x) = - 3 : x = \frac{2 π}{3} + πn

tan (x) = 3 : x = \frac{π}{3} + πn

Combine all the solutions

x = πn, x = \frac{2 π}{3} + πn, x = \frac{π}{3} + πn

2 cos (x) = 2 cos (2 x)

6 sin (2 x) = 3

- cos (x) = - sin^{2} (x) - 1, 0 \leq x \leq 2 π

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

tan (t) = 4

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