Sin(X-y)sin(x+y)=sin^2 x - sin^2 y

work on one side only...so i worked on the right

=(sinx-siny)(sinx+siny) does that equal
sin(x-y)sin(x+y)??? help!

Duplicate post; already answered.

Refer to your previous post.

To determine if (sinx-siny)(sinx+siny) is equal to sin(x-y)sin(x+y), you can use the identity for the difference of squares, which states that (a-b)(a+b) is equal to a^2 - b^2.

Using this identity, let's apply it to (sinx-siny)(sinx+siny):

= (sinx)^2 - (siny)^2

Now, let's compare this expression to the right side of the given equation:
sin^2 x - sin^2 y

We can see that the expressions are indeed equal.

Therefore, (sinx-siny)(sinx+siny) is equal to sin(x-y)sin(x+y).