Question

find the principal value of tan-1( -√3) + tan-1 (1)​

Answer 1

Let tan−1(−1)=θ

⇒tanθ=−1

⇒tanθ=tan4π

tanθ=tan(−4π)⇒θ=−4π

⇒tan−1=−4π

∴ Principal value of tan−1(−1) is −4π.

[∴−4π∈(−2π,2π)rangeoftheprincipalvaluebranchoftan−1functionandtan(4π=−1)]

Answer 2

Refer the attachment!

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