Now put x=0,
That didn't come from anywhere, we multiplied by it to get a solution. To see such things you have to be familiar with trigonometric limits and identities.
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
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.