Find the third-order Fourier approximation to cos^3(t)

Find the third-order Fourier approximation to cos^3(t), without performing any integration calculation

cos^3(x) = cos^2(x) * cos x
.............= (1/2)(1 + cos(2x)) * cos x
.............= (1/2)(cos x + cos(2x) cos x)
.............= (1/2)[cos x + (1/2) (cos(2x - x) + cos(2x + x))]
.............= (3/4) cos x + (1/4) cos(3x).

I hope this helps!