Evaluate tan-1(tan 4)

Given tan^-1(tan 4)

As tan^-1(tan x) = x if x ϵ [\( \dfrac{-\pi}{2},\dfrac{\pi}{2}\)]

But here x = 4 which does not belongs to above range

We also have tan (π – θ) = –tan (θ)

Therefore tan (θ – π) = tan (θ)

Tan (4 – π) = tan (4)

Now 4 – π is in the given range

Hence tan^–1 (tan 2) = 4 – π