Sum and Difference Identities

In this lesson, we will look at the sum identities and difference identities and how to use them to prove other 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

Diferrence 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

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

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Trigonometry