Trig

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!

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  1. 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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