Fourier series for sin(2x) + cos(5x)

I am having trouble finding the real and complex Fourier series for the following:

sin(2x) + cos(5x)

If someone could do the first few steps, I'm sure I could manage the rest.

So for a_n = 1/2pi x integral of (sin(2x)cos(kx) + cos(5x)cos(kx)) between 0, 2pi.... I'm not sure how to manipulate the equation (Speechless)

Am I supposed to use the following: cos(A)cos(B) = (1/2)(cos(A+B) - cos(A-B))?

Kindest regards <3

Hey katspaws.

Use your hint plus the fact sin(kx)cos(mx) is 0 because they are orthogonal if m and k integers.