Hi, ive been given the following problem:
We know that, for all z in C, cos2(z)+sin2(z) = 1.
This does not imply that |cos(z)| =< 1 and |sin(z)|=< 1.
Show in fact that, for all y in R,
|cos(iy)| > 1/2exp(|y|), |sin(iy)| >= 1/2(exp(|y|)-1)
i've managed to show the first part with |cos(iy)|, but dont know how to proceed with the second part, |sin(iy)|, any help would be great!!