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.