Prove that e^ia + 2e^ib = re^ic?

[tommykhoa]

Homework Statement

Prove that e^ia + 2e^ib = re^ic?

Homework Equations

given : r^2 = 5 + 4cos( a - b )
tan c = (sin a + 2 sin b) / (cos a + 2 cos b)
i is imaginary number

The Attempt at a Solution

I tried to expand e^ia + 2e^ib and make it equal to r^2
but I don't know what to do with the tan c

 

[D H]

but I don't know what to do with the tan c

What's wrong with arctangent?