Hi

I'm having serious trouble with trig limits and I'm wondering if anyone could explain it to me in simple terms as I don't really understand the textbook I have. Any help would be greatly appreciated.

For example in my textbook there is an example however I don't understand it. Could any help and just talk us through it?

lim x approaches 0 (1 - cos x)/x = lim x app 0 ((1 - cos x) / x (1 + cos x)/ 1 + cos x)

I don't understand where the 1 + cos x divided by x came from

then it goes on

= 1 - cos^2 x / x(1 + cos x)

= sin^2 x/ x (1 + cos x)

= (sin x/x * sinx x /(1 + cos x))

= sinx x * lim x app 0 sin x/(1 + cos x)

= 1 * sin 0/1 + cos 0

= 0

I can't follow it through so if anyone can explain the steps and tell me how you get that it would ease my troubles. Thanks.