Question

How do you simplify `sin(alpha+beta)+sin(alpha-beta)`?

Answer 1

`sin(alpha+beta)+sin(alpha-beta)=2*sin(alpha)cos(beta)`

Explanation:

We use the general property
`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(alpha+beta)+sin(alpha-beta)=2*sin(alpha)cos(beta)`
as the two terms in red get cancelled