Evaluate the following:tan-1(tan 4) – InterviewSolution

1.

Evaluate the following:tan-1(tan 4)

Answer»

As, tan ^–1(tan x) = x

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

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.

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