Proving the Identity: sin2(x)-sin2(x)=sin(x+y)sin(x-y)?

[HMFan814]

Homework Statement

Prove this is an identity:
sin²(x)-sin²(x)=sin(x+y)sin(x-y)

Homework Equations

N/A

The Attempt at a Solution

I have made a lot of attempts but can not get one side to equal the other. I know It's something really simple I am missing, but can't figure it out.

 

[Dick]

Clearly, you meant sin(x)^2-sin(y)^2. Use the sum formula for sin(a+b) and sin(a-b) and expand it. Then use cos^2-1=sin^2. Expand again.

 

[HMFan814]

You are correct, I did mean sin²(x) - sin ²(y). And you clearly meant 1-cos²=sin².
Thanks.

 

[Dick]

Right.