cos^–1(cos x) = x

Provided x ϵ [0,π] ≈ [0,3.14]

And in our equation x is 4 which does not lie in the above range.

We know cos[2nπ – x] = cos[x]

∴ cos(2nπ – 12) = cos(12)

Here n = 2.

Also 4π–12 belongs in [0,π]

∴ cos^–1(cos 12) = 4π–12