Fourier Series of: 2sin(4000*pi*t)*sin(46000*pi*t)

[zonedestruct]

Homework Statement

How can i find the magnitude spectra of 2sin(4000*pi*t)*sin(46000*pi*t)

The Attempt at a Solution

im not sure how to go about this question, can someone please give me some help on what i should do. I know that for a square wave i can find the Fourier series coefficients of it by finding the Fourier transform of one period (which is the Fourier transform of standard rect function) and then use G_n = f₀G₁(nf₀). But this question I am not sure if i can do this shortcut method.
please help, thanks.

 

[zonedestruct]

someone please give me some hints

 

[rude man]

Given angles x and y, what is the trigonometric identity relating the sines of these angles to the sum and difference of these angles?