A difficult limit involving trig.

**tttcomrader** · Aug 31st 2006, 10:12 PM

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

**CaptainBlack** · Aug 31st 2006, 10:41 PM

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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