- 1 ( 1 + x ) = - 1 ( 2 (x/2) 2 2 (x/2) ) = - 1 ( 2 ) = 2

Inverse Trigonometric Functions — Class 12 Maths Solution

ncert exercise SA NCERT Ex. 2.2, Q. 7 , Page 47

Question

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

Step-by-step Solution

${\tan ^{ - 1}}\left( {\sqrt {\frac{{1 - \cos x}}{{1 + \cos x}}} } \right) = {\tan ^{ - 1}}\left( {\sqrt {\frac{{2{{\sin }^2}(x/2)}}{{2{{\cos }^2}(x/2)}}} } \right)$
$= {\tan ^{ - 1}}\left( {\tan \frac{x}{2}} \right) = \frac{x}{2}$

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