OML Search

Sum and Difference Identities



In these lessons, 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


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

Difference Identities

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

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





 


Example:



Solution:

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



Example:


Solution:





 

Videos

Introduction to sum and difference identities for sin, cos, and tan.


Other examples of Using Sum and Difference Identities



 

Using 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.

OML Search

We welcome your feedback, comments and questions about this site or page. Please submit your feedback or enquiries via our Feedback page.

[?] Subscribe To This Site

XML RSS
follow us in feedly
Add to My Yahoo!
Add to My MSN
Subscribe with Bloglines



Math TutorsMath Tutors