How do you simplify sin(alpha+beta)+sin(alpha-beta)sin(α+β)+sin(α−β)?

1 Answer
Sid P.
Sep 2, 2016

sin(alpha+beta)+sin(alpha-beta)=2*sin(alpha)cos(beta)sin(α+β)+sin(α−β)=2⋅sin(α)cos(β)

Explanation:

We use the general property
sin(a+b)=sin(a)cos(b)+sin(b)cos(a)sin(a+b)=sin(a)cos(b)+sin(b)cos(a)

So, simplifying the above expression using the property, we get;
sin(alpha+beta)+sin(alpha-beta)=sin(alpha)cos(beta)+color(red)(sin(beta)cos(alpha)) + sin(alpha)cos(beta)-color(red)(sin(beta)cos(alpha))sin(α+β)+sin(α−β)=sin(α)cos(β)+sin(β)cos(α)+sin(α)cos(β)−sin(β)cos(α)
:. sin(alpha+beta)+sin(alpha-beta)=2*sin(alpha)cos(beta)
as the two terms in red get cancelled

Related questions
See all questions in Sum and Difference Identities
Impact of this question
16331 views around the world
You can reuse this answer
Creative Commons License