What is the general solution for 15tan^3(x)=5tan(x) ?

The general solution for 15tan^3(x)=5tan(x) is x=pin,x=(5pi)/6+pin,x= pi/6+pin

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15tan^3(x)=5tan(x)

15 tan^{3} (x) = 5 tan (x)

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

Solution steps

15 tan^{3} (x) = 5 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

(cot (θ) + 1) (sin (θ) - 1) = 0

sec (2 x) = tan (2 x) + 1

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

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

sin (x) = cos (x) + 1

What is the general solution for 15tan^3(x)=5tan(x) ?
The general solution for 15tan^3(x)=5tan(x) is x=pin,x=(5pi)/6+pin,x= pi/6+pin