Write the function in the simplest form: tan^{- 1} 1/(√x² - 1), |x| > 1

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 x = cosec θ

⇒ θ = cosec^{- 1} x

Hence,

tan^{- 1} 1 / (√x² - 1)

Using trigonometric identity 

= tan^{- 1} 1 / (√cosec ² θ - 1)

= tan^{- 1} (1/cot θ)

= tan^{- 1} (tan θ)

= θ

= cosec ^{- 1} x

= π/2 - sec^{- 1} x

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NCERT Solutions for Class 12 Maths - Chapter 2 Exercise 2.2 Question 6

Write the function in the simplest form: tan^{- 1} 1/(√x² - 1), |x| > 1

Summary:

The function in the simplest form: tan^{- 1} 1/(√x² - 1), |x| > 1 can be expressed as π/2 - sec^{- 1} x