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प्रश्न
Find the principal value of the following: tan-1(– 1)
उत्तर
The principal value branch of tan-1x is `(- π/2, π/2)`
Let tan-1(–1) = α, where `(-pi)/(2) ≤ α ≤ pi/(2)`
∴ tan α = – 1 = `-tan pi/(4)`
∴ tan α = `tan(- pi/4)` ...[ ∵ tan(– θ) = – tan θ]
∴ α = `- pi/(4) ...[ ∵ - pi/2 ≤ - pi/4 ≤ pi/2 ]`
∴ the principal value of tan-1(–1) is `-pi/(4)`.
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