# Prove that tan^{- 1} √x = 1/2 cos^{- 1} [(1 - x)/(1 + x)], x ∈ |0, 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 = tan^{2} θ

Then,

√x = tan θ

θ = tan^{-1}√x

Therefore,

(1 - x) / (1 + x) = (1 - tan^{2} θ)/(1 + tan^{2} θ)

Thus,

RHS = 1/2 cos^{- 1} [(1 - x)/(1 + x)]

= 1/2 cos^{- 1} (cos 2θ)

= 1/2 × θ

= tan^{-1}√x

= LHS

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

## Prove that tan^{- 1} √x = 1/2 cos^{- 1} [(1 - x)/(1 + x)], x ∈ |0, 1|

**Summary:**

Hence we have proved by using inverse trigonometric functions that tan^{- 1} √x = 1/2 cos^{- 1} [(1 - x)/(1 + x)], x ∈ |0, 1|