The question:

Find all solutions of cos(z) = cos(2)

My attempt:

cos(z) = cos(x)cosh(y) - isin(x)sinh(y) = cos(2)

So we need:

sin(x)sinh(y) = 0 [1]

cos(x)cosh(y) = cos(2) [2]

[1] is zero when or y = 0

Substitute into [2]:

Try just y = 0:

So cos(x)cosh(0) = cos(x) which we want to equal cos(2), thus

Try just

So

Case when k is odd:

cosh(y) = -cos(2)

Case when k is even:

cosh(y) = cos(2)

Therefore, y =

So,

But the solution is :/

What am I doing wrong? Thanks.