Find the principal value of tan^-1 (- √3)

Solution:

Inverse trigonometric functions are the inverse ratio of the basic trigonometric ratios. 

Here the basic trigonometric function of Sin θ = y, can be changed to

θ = sin^-1 y

Let

tan^-1 (- √3) = y

Hence,

tan y = - √3

= - tan (π/3)

= tan (- π / 3)

Range of the principal value of tan^-1 (x)

= (- π / 2, π / 2)

Thus,

principal value of tan^-1 (- √3)

= (- π / 3)

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NCERT Solutions for Class 12 Maths - Chapter 2 Exercise 2.1 Question 4

Find the principal value of tan^-1 (- √3)

Summary:

The principal value of tan^-1 (- √3)  = (- π / 3).  Range of the principal value of tan^-1 (x)  = (- π / 2, π / 2)