Question

Find the limit if it exists.

lim x->0 (1-cosx)/sinx

Answer 1

Did you try LH's rule?

Answer 2

probably haven't had that yet is my guess
multiply by \(\frac{x}{x}\) and you should see two limits you know

Answer 3

Multiply numerator and denominator by (1+ cos x).

Pythagorean identity on top. Easy from there.

Answer 4

@NoelGreco that seems to be the cleanest solution. +1.

Answer 5

I agree, thank you!

Answer 6

\[\frac{ (1-\cos ^{2}x) }{ \sin x(1+\cos x) }=\frac{ \sin ^{2}x }{ \sin x(1+\cos x)}=\]

Answer 7

=0, or I'm up too late.

Answer 8

it does, thanks again :)