Sum and Difference Identities



In this lesson, 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.







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