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

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

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

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

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

Solution steps

(tan (x))^{5} - 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

2 cot^{2} (x) + 2 csc^{2} (x) = 1 + 4 csc (x)

sin (2 θ) = cos (θ), 0 \leq θ < 2 π

\frac{3}{2} sec (θ) = 3

4 csc (θ) - 3 = 0

2 cos^{2} (θ) - 10 = - cos (θ) - 9

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