Question

What is the principle value of tan inverse 1 by root 3, cot inverse 1, sec inverse 1, cosec inverse root 2, sin inverse -1 by 2, cos inverse -1by root 2 tan inverse -1 by root 3, cot inverse -1,sec inverse -2, cosec inverse -root 2​

Answer 1

Given :  Tan⁻¹ ( 1/√3)

To Find :  principle value

Solution:

y =  Tan⁻¹ ( 1/√3)

Taking Tan on both Sides

=> Tany =  Tan (Tan⁻¹ ( 1/√3))

=> Tany = 1/√3

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

& Tan( π/6) =  1/√3

=> Tany = Tan(π/6)

=> y = π/6

=> Tan⁻¹ (1/√3)  =π/6

Similarly :

Cot⁻¹ (1 )  =π/4

Sec⁻¹ (1 )  =0

Cosec⁻¹ (√2 )  =π/4

Sin⁻¹ (-1/2 )  = -π/6

Cos⁻¹ (-1/√2 )  =3π/4

Tan⁻¹ ( -1/√3)  = -π/6

Cot⁻¹ (-1 )  = 3π/4

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