Evaluate each of the following: tan^-1(tan 5π/6) + cos^-1{cos(13π/6)}

Question

Evaluate each of the following: 

\(tan^{-1}(tan\frac{5\pi}6)+cos^{-1}\{cos(\frac{13\pi}6)\}\)

Answer 1

Now, 

We know that, for any x ∈ R, \(tan^{-1}\) represent an angle in \((\frac{-\pi}2,\frac{\pi}2)\) whose tangent is x.

\(\therefore tan^{-1}(-\frac{1}{\sqrt3})=-\frac{\pi}6\)

We know that, for any x ∈ [-1, 1], \(tan^{-1}\) represent an angle in (0, π )whose cosine is x.

Therefore, Principle value of 

\(tan^{-1}(tan\frac{5\pi}6)+cos^{-1}\{cos(\frac{13\pi}6)\}\) is 0.