# 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)

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}