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Math Help - Trig Identities

  1. #1
    Junior Member casey_k's Avatar
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    Exclamation Trig Identities

    Can't seem to get this:

    a) 1-tan x/1- cot x = - tan x

    and

    b) 1+ cot x/1+ tan x = cot x
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  2. #2
    Newbie
    Joined
    Nov 2008
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    (:

    1) 1-tanx/1-cotx = -tanx

    Using the Left side

    1-tanx/1-cotx
    = 1-(sinx/cosx)/1-(cosx/sinx)
    = (cosx-sinx/cosx)/(sinx-cosx/sinx)
    = (cosx-sinx)sinx/-(cosx-sinx)cosx
    = sinx/-cosx
    = - tanx

    2) 1-cotx/1-tanx = cotx

    Using the Left hand side

    1+cotx/1+tanx
    = 1+(cosx/sinx)/1+(sinx/cosx)
    = (sinx+cosx/sinx)/(cosx+sinx/cosx)
    = (sinx+cosx)cosx/(sinx+cosx)sinx
    = cosx/sinx
    = cotx

    Using the equation
    tanx=sinx/cosx
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