The standard equation of AM is
\(y\left( t \right) = {A_c}\cos 2\pi {f_c}t(1 + \mu \cos 2\pi {f_m}t)\)…….(1)
From the given equation
y(t) = cos(2πfct) + 0.3 cos(2πfmt) cos(2πfct)
y(t) = cos(2πfct) ( 1 + 0.3 cos(2πfmt))
Comparing with the standard equation in (1)
Ac = 1
μ = 0.3
Hence modulation index of the modulated AM wave is 0.3