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

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

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3tan^3(θ)=tan(θ)

3 tan^{3} (θ) = tan (θ)

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

Solution steps

3 tan^{3} (θ) = tan (θ)

Solve by substitution

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

tan (θ) = 0 : θ = πn

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

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

Combine all the solutions

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

csc^{2} (x) - 4 = 0

cos (\frac{π}{12})

sin^{2} (x) - 1 = 0

cot (6 0^{\circ})

sec^{2} (\frac{π}{2})

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