A modulated signal Cm(t) has the form Cm(t) = 30sin(300πt) + 10(cos(200πt) - cos(400πt)). The carrier frequency fc, the modulating frequency (message frequency) fω, and the modulation index μ are respectively given by:

Amplitude modulated wave is represented as:
y(t) = Asin(2πfct) + Aμsin(2πfct)sin(2πfwt) = Asin(2πfct) + Aμ/2[cos(2π(fc - fw)t) - cos(2π(fc + fw)t)]
Comparing this with the given equation gives:
2πfc = 300π, ⇒ fc = 150 Hz
2π(fc - fw) = 200π, ⇒ fw = 50 Hz
A = 30
Aμ/2 = 10, ⇒ μ = 2/3