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Math Help - Verifying & Proving Trig Identities

  1. #1
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    Verifying & Proving Trig Identities

    Not sure if this is where it goes but yeah :P
    The question is
    (1+tanx)/(1+cotx) = (sinx)/(cosx)

    as in
    1 + tanx sinx
    ______ = _____
    1 + cotx cosx

    Let x be theta

    I am stuck on this question
    I am thankful for any help
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  2. #2
    MHF Contributor harish21's Avatar
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    use tanx = 1/cotx :

    \dfrac{1+\tan(x)}{1+\cot(x)}=\dfrac{1+\tan(x)}{1+\  frac{1}{\tan(x)}}

    rest is pretty straightforward.. show your work if you are stuck
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  3. #3
    MHF Contributor

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    Another way to do this is to change tan and cot into terms of sine and cosine:
    \frac{1+ \frac{sin(x)}{cos(x)}}{1+ \frac{cos(x)}{sin(x)}}.
    Now multiply both numerator and denominator by sin(x)cos(x) to eleminate the "small" fractions.
    Then factor and cancel.
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