Find the principal value of cosec^-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,

cosec^{- 1} (2) = y

Hence,

cosec y = 2 

As we know that

[ cosec π / 6 = 2 ] 

= cosec (π / 6) 

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

= [- π / 2, π / 2] - {0}

Thus,

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

= (π / 6)

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NCERT Solutions for Class 12 Maths - Chapter 2 Exercise 2.1 Question 3

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

Summary:

The principal value of cosec^{- 1} (2)  = (π / 6).  Range of the principal value of cosec^{- 1} (x)  = [- π / 2, π / 2] - {0}