Chapter 13: Inverse Trigonometric Functions

Notes (Solutions) of Chapter 13: Inverse Trigonometric Functions, Text Book of Algebra and Trigonometry Class XI (Mathematics FSc Part 1 or HSSC-I), Punjab Text Book Board, Lahore.

Contents & summary

Introduction
The Inverse Sine Function
The Inverse Cosine Function
Inverse Tangent Function
Inverse Cotangent, Scant and Coscant Functions
Domains and Ranges of Principal Trigonometric Function and Inverse Functions
- Exercise 13.1
Addition and Subtraction Formulas
- Exercise 13.2

Some important formulas

${\sin ^{ - 1}}A + {\sin ^{ - 1}}B = {\sin ^{ - 1}}\left( {A\sqrt {1 - {B^2}} + B\sqrt {1 - {A^2}} } \right)$
${\sin ^{ - 1}}A - {\sin ^{ - 1}}B = {\sin ^{ - 1}}\left( {A\sqrt {1 - {B^2}} - B\sqrt {1 - {A^2}} } \right)$
${\cos ^{ - 1}}A + {\cos ^{ - 1}}B = {\cos ^{ - 1}}\left( {AB - \sqrt {\left( {1 - {A^2}} \right)\left( {1 - {B^2}} \right)} } \right)$
${\cos ^{ - 1}}A - {\cos ^{ - 1}}B = {\cos ^{ - 1}}\left( {AB + \sqrt {\left( {1 - {A^2}} \right)\left( {1 - {B^2}} \right)} } \right)$
$\displaystyle {\tan ^{ - 1}}A + {\tan ^{ - 1}}B = {\tan ^{ - 1}}\frac{{A + B}}{{1 - AB}}$
$\displaystyle{\tan ^{ - 1}}A - {\tan ^{ - 1}}B = {\tan ^{ - 1}}\frac{{A - B}}{{1 + AB}}$