This question appears in my university postgraduate advanced engineering mathematics course:

Show that:

2π

∫ e ^(ρ.cosθ) . cos(ρ sinθ nθ) dθ = 2πρⁿ/n!0

where ρ>0, and n = 1,2,3...

Hint: cos(ρ sinθ nθ)=Re{cos(ρ sinθ nθ) + i sin (ρ sinθ nθ)}

(10 marks)

Thanks a lot in advance. ;-)