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Evaluate each of the following:
tan–1 (tan 12)
As, tan–1(tan x) = x
Provided x ϵ
Here our x is 12 which does not belong to our range
We know tan(nπ –θ) = –tan(θ)
∴ tan(θ –2nπ ) = tan(θ)
Here n = 4
∴ tan(12–4π ) = tan(12)
Now 12–4π is in the given range
∴ tan–1 (tan 12) = 12–4π.