The function f is continuous on the open interval (-π, π). If f(x)=cos(x)-1/xsin(x) for x≠0, what is the value of f(0)?

Answer 1

note that since tan(x/2) = (1-cosx)/sinx, what you have is

f(x) = -tan(x/2)/x
= -1/2 tan(x/2)/(x/2)
lim(x->0) f(x) is thus -1/2