find all the solutions of the trig equation

Question

tanx-3cotx=0

Answer 1

Given that Tanx - 3 cotx = 0

Therefore the solution for the given trignometric equation is

Answer 2

Given trigonometric equation tanx-3cotx=0

tanx-3/tanx = 0

Multiply with tanx on both sides to get,

tan^2(x) - 3 = 0

By adding 3 on both sides , we get 

tan^2(x) = 3

Taking square root on both sides, 

tanx = sqrt(3)

x = tan^(-1)(sqrt3)

x = tan^(-1)(tan60)

x = 60 0r pi/3

 

Comments

tan x = ±√3.

• tan x = - √3.

tan x = tan(2π/3).

The genaral solution of tan(θ) = tan(α) is θ = nπ + α, where n is an integer.

⇒ x = nπ + (2π/3).

• tan x = √3.

tan x = tan(π/3).

The genaral solution of tan(θ) = tan(α) is θ = nπ + α, where n is an integer.

⇒ x = nπ + (π/3).

Therefore, the solutions are x = nπ + (2π/3) and x = nπ + (π/3), where n is an integer.