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Math Help - Proving Identities

  1. #1
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    Proving Identities

    I am still having problems on this proving identity problem:

    tan^2t/sect = sect - cost

    If someone could please help me I would greatly appreciate it.
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  2. #2
    MHF Contributor
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    There.
    Only one. And clear.

    tan^2t/sect = sect - cost

    tan^2(T)/secT = secT -cosT
    We develop the Lefthand Side (LHS) while the RHS stays.
    Convert the tan and sec into sin and/or cos,
    LHS = tan^2(T)/secT
    = [(sinT / cosT)^2] / [1 / cosT]
    = [sin^2(T) / cos^2(T)]*[cosT / 1]
    = sin^2(T) / cosT
    Since sin^2(T) +cos^2(T) = 1, then,
    = [1 -cos^2(T)] / cosT
    = 1/cosT -cos^2(T)/cosT
    = secT -cosT
    And that is the same as the RHS.
    Therefore, proven.
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  3. #3
    vms
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    we have

    Tan^2t=sec^2t - 1

    so
    Tan^2t/sect=(sec^2t - 1 )/sect

    that gives the right hand side as sect - cost
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