Find the value of tan-1 (1) and tan-1 (tan 1)

We need to find the value of tan^-1(1) and tan^-1(tan 1)

Solution

(i) tan-1(tan 1)

Given tan-1(tan 1)

But we have tan-1(tan x) = x if x ϵ [-π/2, π/2]

By substituting this condition in given question

Tan-1(tan 1) = 1

(ii) tan -1 (1)

We know that

tan -1 (1) = tan -1 (tan π/4)

= π/4

Answer

Tan-1(tan 1) = 1

tan -1 (1)= π/4

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