Write the function in the simplest form : tan^{- 1} √(1 - cos x)/(1 + cos x), 0 < x < π

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

As we know that 

1 - cos x------(1)

= 2 sin² x / 2 and

Using trigonometric identity 

1+ cos x = 2 cos² x/2 ------(2)

Given question can be written as 

tan^{- 1} √(1 - cos x)/(1 + cos x)

Using equation 1 and 2

= tan^-1 √(2 sin² x/2) / (2 cos² x/2)

= tan^{- 1} (sin x / 2) / (cos x / 2)

= tan^{- 1}tan x / 2

= x/2

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NCERT Solutions for Class 12 Maths - Chapter 2 Exercise 2.2 Question 7

Write the function in the simplest form : tan^{- 1} √(1 - cos x)/(1 + cos x), 0 < x < π

Summary:

The function in the simplest form : tan^{- 1} √(1 - cos x)/(1 + cos x), 0 < x < π can be written as x/2.Inverse trigonometric functions are the inverse ratio of the basic trigonometric ratios