Thread: Complex Trig function problem

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!!

Attached