Trig/pre-calc question! (tan)?

Question

Find all solutions of the equation tan^5 x – 9 tan x = 0.
The answer is Akpi where k is any integer.


So i tried solving it, and it didn't work out so well. please help! thank you!

Answer 1

Solve for x.
tan^5 x - 9tanx = 0
__________

tan^5 x - 9tanx = tanx(tan^4 x - 9)
= tanx(tan²x + 3)(tan²x - 3)
= tanx(tan²x + 3)(tanx - √3)(tanx + √3) = 0

tanx = 0
tanx = √3
tanx = -√3

x = 0 + πk, π/3 + πk, 2π/3 + πk