# Chapter 14: Solutions of Trigonometric Equation

Notes (Solutions) of Chapter 14: Solutions of Trigonometric Equation, Text Book of Algebra and Trigonometry Class XI (Mathematics FSc Part 1 or HSSC-I), Punjab Text Book Board, Lahore.

### Contents & summary

• Introduction
• Solution of General Trigonometric Equations
• Exercise 14

### Some important formulas

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