Question

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

Answer 1

Step-by-step 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.