# A difficult limit involving trig.

• August 31st 2006, 10:12 PM
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
• August 31st 2006, 10:41 PM
CaptainBlack
Quote:

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

$
\frac{1-\tan(x)}{\sin(x)-\cos(x)} =\frac{1}{-\cos(x)}\frac{(1-tan(x))}{(1-tan(x))}=-\sec(x)
$

so:

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

RonL