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    mwilt's Avatar
    mwilt Posts: 3, Reputation: 1
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    #1

    Mar 4, 2009, 08:59 PM
    trig proofs
    how do you prove

    cosx+sinxtanx=secx
    Perito's Avatar
    Perito Posts: 3,139, Reputation: 150
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    #2

    Mar 5, 2009, 05:55 AM

    The usual way to prove any of these trig identities is to convert everything to sines and cosines and simplify. Sometimes you have to be cleaver.

    cos(x) + sin(x) tan(x) = sec(x)

    identity: tan(x) = sin(x) / cos(x)

    cos(x) + sin(x) * sin(x)/cos(x) = 1/cos(x)
    cos(x) + sin^2(x)/cos(x) = 1/cos(x)
    [cos^2(x) + sin^2(x)] / cos(x) = 1 / cos(x)

    identity: sin^2(x) + cos^2(x) = 1

    identity: sec(x) = 1/cos(x)

    sec(x) = sec(x)

    quod erat demonstrandum

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