- 1 ( x + x ), ;0 < x <

- 1 ( x + x ) = - 1 ( 1 + x ) (Dividing numerator and denominator by cos x) = - 1 ( ( 4 - x ) ) = 4 - x

Inverse Trigonometric Functions — Class 12 Maths Solution

ncert exercise SA NCERT Ex. 2.2, Q. 8 , Page 47

Question

${\tan ^{ - 1}}\left( {\frac{{\cos x - \sin x}}{{\cos x + \sin x}}} \right),\;0 < x < \pi$

Step-by-step Solution

${\tan ^{ - 1}}\left( {\frac{{\cos x - \sin x}}{{\cos x + \sin x}}} \right) = {\tan ^{ - 1}}\left( {\frac{{1 - \tan x}}{{1 + \tan x}}} \right)$

(Dividing numerator and denominator by cos x)

$= {\tan ^{ - 1}}\left( {\tan \left( {\frac{\pi }{4} - x} \right)} \right) = \frac{\pi }{4} - x$

NCERT & Exemplar solution for CBSE Class 12 Mathematics, Inverse Trigonometric Functions. Curated by Sachin Sharma. Free for all students.