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sec^2A+tan^2A=(1-sin^4A)sec^4A

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  1. since sec^2-tan^2=1, you can multiply by that:

    (sec^2+tan^2)(sec^2-tan^2)
    sec^4-tan^4
    but, since tan=sin/cos = sin*sec, that's

    sec^4-sin^4*sec^4
    (1-sin^4)sec^4

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