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Radians & Degrees

Angles in Standard Position Revisited

Trig. Functions & Graphs

Transformations

Trig. Identities

Trig. Equations

Summary&Test

LESSON 5:SOLVING TRIGONOMETRIC IDENTITIES

 

jdsmathnotes

 


Definition: An Identity is a mathematical statement that is true for all variables in the given domain.

 

Example 1: x2 + x = x(x + 1)

This statement is an identity as it is true for all x in the real number system

 

Proof: We prove this by showing that the Left side of the equation equals the Right side.

 

L.S. = x2 + x R.S. = x(x + 1)

= x2 + x

Therefore L.S. = R.S. and the identity is proven.

 

Basic Trigonometric Identities :

 

1. Quotient Identity:

 

2. Pythagorean Identities:

 

Example 2:

 

Proof:

 

Text Box: Strategies for Proving Trig. Identities
1.	Start with the most complex side.  You may, however work on either side.
2.	Change any tan x expression to sin x and cos x using the quotient identity.
3.	Simplify algebraically using expanding or factoring where appropriate
4.	Use rules of fractions where needed  common denominators, multiplication and division rules for fractions.
5.	If sin2x or cos2x occurs, use the Pythagorean identities if they simplify the expression.
 

 

 

 

 

 

 

 

 

 


Example 3:

 

Proof:

 

Example 4:

 

 

Proof:

 

 

 

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