Find the principal value of cosec^{- 1} (- √2)

Solution:

Inverse trigonometric functions as a topic of learning are closely related to the basic trigonometric ratios.

The domain (θ  value)  and the range(answer) of the trigonometric ratio are changed to the range and domain of the inverse trigonometric function.

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,

cosec^{- 1} (- √2) = y

Hence,

cosec y = - √2

= - cosec (π / 4)

= cosec (- π / 4)

Range of the principal value of cosec^{- 1} (x)

= [- π / 2, π / 2] - {0}

Thus,

principal value of cosec^-1 (- √2)

= (- π/4)

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NCERT Solutions for Class 12 Maths - Chapter 2 Exercise 2.1 Question 10

Find the principal value of cosec^{- 1} (- √2)

Summary:

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