Using the convolution property, find the spectrum for
$$w(t)= \sin(2\pi f_1 t) \cos(2\pi f_2 t).$$
I'm confused on how to solve this question. Can you give me any aproach?
The Fourier Transform of the product of two signals (functions) is the convolution of their spectra, i.e. the convolution of their individual Fourier Transforms. The spectra of $sin(2\pi f_1t), cos(2 \pi f_2t)$ are well known (dirac functions at appropriate locations and with appropriate coefficients) and convolving them is also easy, using the property of the delta function $\delta(t-t_0) * f(t)=f(t_0)$ where $*$ denotes convolution.