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Sum and Difference Identities




In these lessons, solutions, and examples we will learn
  • the sum identities and difference identities for sine, cosine and tangent.
  • how to use the sum identities and difference identities to simplify trigonometric expressions.
  • how to use the sum identities and difference identities to prove other trigonometric identities.

Related Topics: More Trigonometric Identities

What are the Sum and Difference Identities?
The Sum and Difference Identities for sin, cos and tan are as follows.

Sum Identities

sin (a + b) = sin a cos b + cos a sin b

cos (a + b) = cos a cos b – sin a sin b

sum identities

Difference Identities

sin (a - b) = sin a cos b - cos a sin b

cos (a - b) = cos a cos b + sin a sin b

difference identities


Example:



Solution:

Given that cos(α + β) = cos α cos β – sin α sin β, then



Example:


Solution:





Introduction to sum and difference identities for sin, cos, and tan.
Other examples of Using Sum and Difference Identities


 
How to use the Sum and Difference Identities to Prove Other Identities
Using the Sum and Difference Identities for Sine, Cosine and Tangent, Ex 1.


Using the Sum and Difference Identities for Sine, Cosine and Tangent, Ex 2.
Using the Sum and Difference Identities for Sine, Cosine and Tangent, Ex 3.


 

You can use the Mathway widget below to practice Trigonometry or other math topics. Try the given examples, or type in your own problem. Then click "Answer" to check your answer.

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