Write the function in the simplest form : tan^{- 1} √(cosx - sin x)/(cos x + sin 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

Using trigonometric identity 

tan^{- 1} √(cos x - sin x) / (cos x + sin x)

On dividing numerator and denominator by cos x, we get

= tan^{- 1} [((cos x - sin x) / cos x) / ((cos x + sin x) / cos x)]

= tan^{- 1} [(1 - (sin x) / (cos x)) / (1 + (sin x) / cos x))]

Since ,

sin x / cos x = tan x

we get,

= tan^{- 1} [(1 - tan x) / (1 + tan x)]

= tan^{- 1} (1) - tan^{- 1} (tan x)

= π / 4 - x

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NCERT Solutions for Class 12 Maths - Chapter 2 Exercise 2.2 Question 8

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

Summary:

The function in the simplest form : tan^{- 1} √(cosx - sin x)/(cos x + sin x), 0 < x < π can be expressed as π / 4 - x