find the limit as f(x) approaches 0?

Question

f(x)=cos(2x)-1/cosx-1
i know the answer is -1 can anyone get the work?

Answer 1

f(x)
= [cos(2x)-1]/[cosx-1]
= -2sin^2(x)/[-2sin^2(x/2)]
Therefore the limit of f(x) as x->0 is 4.

Answer 2

As x==>0 and if the parenthesis are right
lim [(cox2x-1)/(cosx-1)= lim -2sin 2x /-sin x = 4 (using L´Hôpital)
By using Taylor
cos 2x = 1 -1/2(2x)^2+++
cos x= 1-1/2 x^2+++ so (cos 2x-1)/(cosx-1) => 4