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.
sin (a + b) = sin a cos b + cos a sin b
cos (a + b) = cos a cos b – sin a sin b
sin (a - b) = sin a cos b - cos a sin b
cos (a - b) = cos a cos b + sin a sin b
Given that cos(α + β) = cos α cos β – sin α sin β, then
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.
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