Trigonometric Deduction from Euler's Formula: Finding the Correct Relations

[Hymne]

Anybody that can show how to deduce
cos(a+b) = cos(a)cos(b) - sin(a)sin(b)
sin(a+b) = sin(a)cos(b) + sin(b)cos(a)
From the relations that we get from eulers formula..
Should be really simple but I think that I have got some relations wrong so I need to se the real solution.
Thanks!

 

[neutrino]

Which relations have you got wrong?

 

[morson]

Your relations are fine. Use this to verify it:

$$cos(a + b) = Re[cis(a)cis(b)]$$
$$sin(a + b) = Im[cis(a)cis(b)]$$

 

[Hymne]

Which relations have you got wrong?

Hehe it turned out to be that I had it all right I had just made a stupid misstake and was to close to detect it.
Thanks for the help, both of you.