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Question

Find the principal values of the following questions:

tan1(3)

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Solution

Let tan1(3)=θtanθ=3
We know that the range of principal value of tan1 θ is (π2,π2).
tanθ=3=tanπ3=tan(π3) ( tan(θ)=tanθ)
θ=π3, where θϵ(π2,π2)tan1(3)=π3
Hence, principal value of tan1(3) is π3


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