What is the general solution for tan^5(x)-9tan(x)=0 ?

The general solution for tan^5(x)-9tan(x)=0 is x=pin,x=(2pi)/3+pin,x= pi/3+pin

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tan^5(x)-9tan(x)=0

tan^{5} (x) - 9 tan (x) = 0

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

Solution steps

tan^{5} (x) - 9 tan (x) = 0

Solve by substitution

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

tan (x) = 0 : x = πn

tan (x) = 3 i :

No Solution

tan (x) = - 3 i :

No Solution

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

1 - cos (θ) = \frac{1}{2}

(tan (θ) - 1) (cos (θ) + 1) = 0

sin^{2} (θ) = cos^{2} (θ)

x, sin (x) = 0

cos (θ) = \frac{2}{5}

What is the general solution for tan^5(x)-9tan(x)=0 ?
The general solution for tan^5(x)-9tan(x)=0 is x=pin,x=(2pi)/3+pin,x= pi/3+pin