find the period

Question

find the fundamental period of the function f(x) =tan^-1(tanx) - tan^-1(cotx).

Answer 1

Given function is f(x) = tan^-1(tan x) - tan^-1(cot x)

∵ tan(π + x) = tan x and cot(π + x) = cot x

∴ f(π + x) = tan^-1[tan(π + x)] - tan^-1[cot(π + x)]

= tan^-1(tan x) - tan^-1(cot x)

= f(x)

Hence, f(π + x) = f(x)

Therefore the fundmental period 8 function

f(x) is π.