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6.2 TRIGONOMETRIC EQUATIONS

Equations involving trigonometric functions of unknown angles are called

1) identities, if they are satisfied by all values of the unknown angles for which the
trigonometric functions are defined.

2) Conditional equations which are satisfied by particular values of the unknown angles.

A Solution is a value of the angle which satisfies a given trigonometric equation.

Solution in a particular interval, such as 0 £ x £ 2p are usually known as "primary
solution"
.

A general solution is that formula which lists all possible solutions.

No clear - cut procedure of solving general trigonometric equation exist. It involves the use of identities, algebraic manipulation, trial and error etc. Some standard procedures are given below.

1) Factoring (2) Squaring both sides (3) Expressing various functions in terms of single function .

Example 1

Solve sin x - sin 2x = 0

Solution : sin x - sin 2x = 0



Example 2

Solve : sin 4x - sin 2x = 0

Solution : sin 4x - sin 2x = 0

sin 4x = sin 2x

Now putting n = 0, 1, 2, ... the values of in the range 0 £ £ 2 p gives the primary solution.

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Index

6.1 Inverse Functions
6.2 Trignometric Equations
Supplementary Problems

Chapter 7

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