Question

Write the principal value of tan-¹(-1).

Answer 1

Given :  tan-¹(-1).

To find : principal value of tan-¹(-1).

Solution:

principal value of tan-¹(-1).

Let say  

y =  Tan⁻¹ ( - 1)

Taking Tan on both Sides

=> Tany =  Tan (Tan⁻¹ ( - 1))

=> Tany = -1

We know that Principle Range of Tan⁻¹ is  ( -π/2 , π/2)

& Tan(-π/4) =  - 1

=> Tany = Tan(-π/4)

=> y = -π/4

=> Tan⁻¹ ( - 1)  = -π/4

Learn more:

"cos⁻¹(-1/2 ) का मुख्य मान ज्ञात कीजिये"

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cos⁻¹ (½) + 2sin⁻¹(½) का मान ज्ञात कीजिये

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