Q.A frequency modulated signal is given by 75sin[2π×90×10⁶t+6sin200πt] Determine

Reading the carrier and modulating angular terms from the given wave, plus the modulation index from the inner-sine coefficient, gives every quantity; the deviation is $m_f f_m$. …

[!TLDR]

Comparing with the standard FM form gives $f_m = 100\ \text{Hz}$, $f_c = 90\ \text{MHz}$, $m_f = 6$ and $\Delta f = 600\ \text{Hz}$.

Compare $75\sin[2\pi\times90\times10^{6}t + 6\sin(200\pi t)]$ with $v = V_c\sin(\omega_c t + m_f\sin\omega_m t)$.

1. The inner modulating term is $200\pi t = 2\pi f_m t$, so $f_m = \dfrac{200\pi}{2\pi} = 100\ \text{Hz}$.
2. The carrier term is $2\pi\times90\times10^{6}t$, so $f_c = 90\times10^{6} = 90\ \text{MHz}$. …