What is the general solution for tan^3(x)= 1/3 tan(x) ?

The general solution for tan^3(x)= 1/3 tan(x) is x=pin,x=-0.52359…+pin,x=0.52359…+pin

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tan^3(x)= 1/3 tan(x)

tan^{3} (x) = \frac{1}{3} tan (x)

x = πn, x = - 0.52359 \dots + πn, x = 0.52359 \dots + πn

Solution steps

tan^{3} (x) = \frac{1}{3} tan (x)

Solve by substitution

tan (x) = 0, tan (x) = - \frac{1}{3}, tan (x) = \frac{1}{3}

tan (x) = 0 : x = πn

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

tan (x) = \frac{1}{3} : x = arctan (\frac{1}{3}) + πn

Combine all the solutions

x = πn, x = arctan (- \frac{1}{3}) + πn, x = arctan (\frac{1}{3}) + πn

Show solutions in decimal form

x = πn, x = - 0.52359 \dots + πn, x = 0.52359 \dots + πn

cos^{2} (x) = \frac{2}{3}

5 ∣ tan (x) ∣ = 5

3 arccos (x) = 2

cos (4 x) = - \frac{1}{2}, 0 \leq x \leq 2 π

3 csc^{2} (x) + 1.5 cot (x) = 15

What is the general solution for tan^3(x)= 1/3 tan(x) ?
The general solution for tan^3(x)= 1/3 tan(x) is x=pin,x=-0.52359…+pin,x=0.52359…+pin