Question

Evaluate of the following:

tan^-1(tan 2)

Answer 1

As, tan^-1(tan x) = x

Provided x ∈ \((\frac{-\pi}2,\frac{\pi}2)\)

Here our x is 2 which does not belong to our range

We know tan (π - θ) = -tan(θ)

\(\therefore\) tan (θ - π) = tan(θ)

\(\therefore\) tan (2 - π) = tan(2)

Now 2 - π is in the given range

\(\therefore\) tan^-1(tan 2) = 2 - π