Find the principal value of tan^{-1}(cos(\dfrac{\pi}{2}))

Given that \( tan^{-1} (cos (\dfrac{\pi}{2}))\)

But we know that \( cos (\dfrac{\pi}{2}) = 0\)

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

Therefore tan^-1 (0) = 0

Hence the principal value of \( tan^{-1} (cos (\dfrac{\pi}{2}))\) is 0.