What is the general solution for 6tan^3(x)=2tan(x) ?

The general solution for 6tan^3(x)=2tan(x) is x=pin,x=(5pi)/6+pin,x= pi/6+pin

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6tan^3(x)=2tan(x)

6 tan^{3} (x) = 2 tan (x)

x = πn, x = \frac{5 π}{6} + πn, x = \frac{π}{6} + πn

Solution steps

6 tan^{3} (x) = 2 tan (x)

Solve by substitution

tan (x) = 0, tan (x) = - \frac{3}{3}, tan (x) = \frac{3}{3}

tan (x) = 0 : x = πn

tan (x) = - \frac{3}{3} : x = \frac{5 π}{6} + πn

tan (x) = \frac{3}{3} : x = \frac{π}{6} + πn

Combine all the solutions

x = πn, x = \frac{5 π}{6} + πn, x = \frac{π}{6} + πn

tan^{2} (θ) = tan (θ)

sin (2 θ) = - sin (θ)

sin (x) = 2

cos^{2} (θ) - 1 = 0

sin (x + \frac{π}{4}) + sin (x - \frac{π}{4}) = 1

What is the general solution for 6tan^3(x)=2tan(x) ?
The general solution for 6tan^3(x)=2tan(x) is x=pin,x=(5pi)/6+pin,x= pi/6+pin