Posted by Alice on Saturday, February 21, 2009 at 4:23pm.
Use the formulas for sin (A-B) and sin (A+B)
The left side is
(sinx cos y - siny cosx)(sinx cosy + siny cosx)
= sin^2x cos^2y - sin^2y cos^2 x
=(1 - cos^2x)(cos^2y)-sin^2y cos^2x
= cos^2y -cos^2y cos^2x - sin^2y cos^2x
= cos^2y -cos^2x
= 1-sin^2y -1 + sin^2x
= sin^2x - sin^2y
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