Limit Evaluation for (1-tan x) / (sin x - cos x) as x approaches pi/4

[meeklobraca]

Homework Statement

lim (1-tan x) / (sin x - cos x)
x-->pi/4

Homework Equations

The Attempt at a Solution

Im not sure where to start with this one. Should I turn tan x into sinx/cos x and try to do cancel some of the equation out?

 

[Mark44]

That might work. Another approach is L'Hopital's Rule if you know it, since this expression has the indeterminate form 0/0.

 

[AEM]

Homework Statement

Im not sure where to start with this one. Should I turn tan x into sinx/cos x and try to do cancel some of the equation out?

I just tried what you suggest and it came out okay.

 

[meeklobraca]

Well I did some work with the equation and got 2/sqrt 2

This is how I got there,

I made the 1 = cos x/cos x
The tan x = sin x/cos x

Then I brought the denomenator up which canceled out both sin x - cos x which left me with 1 / -cos x

I plugged in the pi/4 which is sqrt 2/2 , which equals -2/sqrt2, which equals -sqrt2

What do you guys think?