Using appropriate Fourier-transform theorems and pairs, express the spectrum Y(f) of y(t) = x(t) cos ( 0

Using appropriate Fourier-transform theorems and pairs, express the spectrum Y(f) of 

y(t) = x(t) cos (ω₀t) + x̂(t) sin (ω₀t)

in terms of the spectrum X(f) of x(t), where X(f) is low pass with bandwidth

B < f₀ = ω₀ / 2π

Sketch Y(f) for a typical X(f).