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

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The discussion revolves around proving the identity sin²(x) - sin²(y) = sin(x+y)sin(x-y). Participants clarify that the original statement mistakenly used sin²(x) instead of sin²(y). They suggest using the sum and difference formulas for sine and expanding the expressions. The conversation emphasizes the need to apply the identity cos² - 1 = sin² for further simplification. Ultimately, the focus is on correcting the initial misunderstanding to successfully prove the identity.
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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.
 
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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.
 
You are correct, I did mean sin2(x) - sin 2(y). And you clearly meant 1-cos2=sin2.
Thanks.
 
Right.
 

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