Solving a Limit Involving tanx and pi/4

[Glissando]

Homework Statement

Find the limit:

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

Homework Equations

tanx = sinx/cosx

The Attempt at a Solution

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

lim [(sinx-cosx)/cosx]/(x-pi/4)
x->pi/4

I have no idea what to do after this ): I also tried squaring the whole function and getting tan²x-1 = sec²x, but I get so lost on what to do with pi/4 because it just keeps becoming undefined!

Thanks for your help!

 

[micromass]

Hi Glissando!

I take it you're not allowed to use l'hospital's rule?? In that case, I would first write

$$\tan(x)=\tan((x-\pi/4)+\pi/4)$$

and work that out. That way you can write everything in function of $x-\pi/4$.

 

[Glissando]

Hi Glissando!

I take it you're not allowed to use l'hospital's rule?? In that case, I would first write

$$\tan(x)=\tan((x-\pi/4)+\pi/4)$$

and work that out. That way you can write everything in function of $x-\pi/4$.

Hi micromass,

Thanks for your quick response! I'm not too sure what you mean by working it out...do I plug that back into the original equation? Am I solving for x?

Thanks!

 

[micromass]

Well, you know formula's for $\tan(\alpha+\beta)$. So apply these formula's on

$$\tan((x-\pi/4)+\pi/4)$$

Our goal is to write everything in function of $x-\pi/4$