SOLUTION: Could anyone please prove this: sin(x+y)sin(x-y)=cos^2(y)-cos^2(x) *involves adding and subtracting formulas. Pick only one side to do.

Question 924818: Could anyone please prove this: sin(x+y)sin(x-y)=cos^2(y)-cos^2(x) *involves adding and subtracting formulas. Pick only one side to do.
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
sin(x+y)sin(x-y)=cos^2(y)-cos^2(x)
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Using the left side::
[sin(x)cos(y)+cos(x)sin(y)][sin(x)cos(y)-cos(x)sin(y)]
----
= [sin^2(x)cos^2y) - cos^2(x)sin^2(y)]
----
= [(1-cos^2(x))cos^2(y) - cos^2(x)(1-cos^2(y)]
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= [cos^2(y) - cos^2(x)cos^2(y) - cos^2(x) + cos^2(x)cos^2(y)]
-----
= cos^2(y) - cos^2(x)
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Cheers,
Stan H.
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