How do I solve (cos(pi/3 +h) - 1/2)/ h as h -- 0 but without lhopitals rule

Question

How do I solve (cos(pi/3  +h) -  1/2)/ h     as h --> 0    but without lhopitals rule

psymon · Answer

Okay, 3 things we have to be aware of that will help us get the answer. First we need to know two identities:

$$\lim_{x \rightarrow 0}\frac{ sinx }{ x }=1$$
$$\lim_{x \rightarrow 0}\frac{ cosx - 1 }{ kx }=0$$where k can be any number. So with those two identities being known, use the sum of cosines identity and expand the cos(pi/3 + h) expression, then try to manipulate things so you can use thw 2 identities above.