Question

Sin(x-y)+sin(x-y prove the identity

Answer 1

Explanation:

`\sin(x - y) + \sin(x + y) = 2 \sin(x) \cos(y)`

We use the sum and difference identities.

Remeber the sum difference identity is

`\sin(x + y) = \sin(x) \cos(y) + \cos( x ) \sin(y)`

and

`\sin(x - y) = \sin(x) \cos(y) - \sin(x) \cos(y)`

So we get

`(\sin(x) \cos(y) - \sin(y) \cos(x) ) + \sin(x) \cos(y) + \sin(y) \cos(x)`

Combine like Terms.

`2 \sin(x) \cos(y) = 2 \sin(x) \cos(y)`

We have provided it.