Math

SinAsin2A+sin3Asin6A/sinAcos2A+sin3Acos6A

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  1. using your product-to-sum formulas,
    sinA sin2A = 1/2 (cosA-cos3A)
    sin3A sin6A = 1/2 (cos3A-cos9A)
    and so on ...

    so your fraction now is

    (cosA-cos3A)+(cos3A-cos9A)
    -------------------------------
    (cos3A-sinA)+(sin9A-sin3A)

    = (cosA-cos9A)/(sin9A-sinA)

    now go back the other way using sun-to-product formulas, and simplify

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