Find the principal value of cos^-1 (- 1/√2)

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,

cos^-1 (- 1/√2) = y

Hence,

cos y = - 1/√2

= - cos (π / 4)

= cos (- π / 4)

= cos (π - π / 4)

= cos (3π / 4)

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

= [0, π]

Thus,

principal value of cos^-1 (- 1/√2)

= (3π / 4)

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NCERT Solutions for Class 12 Maths - Chapter 2 Exercise 2.1 Question 9

Find the principal value of cos^-1 (- 1/√2)

Summary:

The principal value of cos^-1 (- 1/√2)  = (3π / 4). Range of the principal value of cos^-1 (x) = [0, π]