deriviative of tan x proof using limits

[Guest]

can someone help me prove the derivative of tan x using the limit process...please?
i know how to prove it by using sin and cos; however i am having trouble proving it via the limit process

here's how far i got

lim (tan (x +h)-tan(x)/h
lim (sin (x+h)/cos(x+h))-sin(x)/cos(x))/h

ierno where to take it from there... O_O

 

[stapel]

While converting to sines and cosines is often helpful, in this case, I would stick with the tangent. Use the angle-sum formula for tangents, and simplify the fraction. You should get something that rearranges nicely into something you can work with. :wink:

Eliz.