- 1 ( - x 2 ), ;|x| ; < a

Put x = asin we get : tan -1 ( acos ) = tan -1 (tan ) = = sin -1 ( a )

Inverse Trigonometric Functions — Class 12 Maths Solution

ncert exercise SA NCERT Ex. 2.2, Q. 9 , Page 48

Question

${\tan ^{ - 1}}\left( {\frac{x}{{\sqrt {{a^2} - {x^2}} }}} \right),\;|x|\; < a$

Step-by-step Solution

Put x = $asin\theta$ we get :

$tan^{-1}( \frac{asin\theta}{acos\theta} )$

$= tan^{-1}(tan\theta) = \theta$

$= sin^{-1}(\frac{x}{a} )$

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