Question

Find the general solution of the following equation: 

tan³ x – 3tan x = 0

Answer 1

To Find: General solution.

Given: tan³x - 3tanx = 0

⇒ tan x (tan² x - 3) = 0

⇒ tan x = 0 or tan x = ± √3

⇒ tan x = 0 or tan x = (π/3) or tan x = tan (2π/3)

Formula used: tan θ = 0 

⇒ θ = nπ, n ∈ l, tan θ = tan α

⇒ θ = kπ ± α, k ∈ l

So x = nπ or x = kπ + π/3 or x pπ + 2π/3 where n, k, p ∈ l

So general solution is x = nπ or x = kπ + π/3 or x = pπ + 2π/3 where n, k, p ∈ l