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Math Help - A difficult limit involving trig.

  1. #1
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    A difficult limit involving trig.

    lim (1-tanx)/(sinx-cosx)
    x->pi/4

    I had been trying for 20 mins, but still cannot find a way to solve it as both top and bottom goes to 0...

    Thank you.

    KK
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by tttcomrader
    lim (1-tanx)/(sinx-cosx)
    x->pi/4

    I had been trying for 20 mins, but still cannot find a way to solve it as both top and bottom goes to 0...

    Thank you.

    KK
    <br />
\frac{1-\tan(x)}{\sin(x)-\cos(x)} =\frac{1}{-\cos(x)}\frac{(1-tan(x))}{(1-tan(x))}=-\sec(x)<br />

    so:

    <br />
\lim_{x \to \pi/4} \frac{1-\tan(x)}{\sin(x)-\cos(x)} = \lim_{x \to \pi/4} -\sec(x)<br />

    RonL
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