In the clamper circuit, consider \$V_{i} = V_{p}cos(\omega t)\$, and consider only the first quarter of \$V_{i}\$ i.e from \$\omega t=0\$ to \$\pi/2\$:
(Assumption: Initial charge on capacitor is zero and diode is ideal)
Assuming diode to be reverse biased, then \$V_d\$ must be negative, otherwise the assumption is false.
\$V_d = -V_{i} + v_c = -V_{m}cost(\omega t) + 0 =\$ -ve from \$\omega t=0\$ to \$\pi /2\$ so the diode is indeed reverse biased.
This time assuming the diode to be forward biased, then the current \$I_d\$ must be positive, otherwise the assumption is false.
Now \$I_d = -C\frac{dv_c}{dt} = -C\frac{dV_{i}}{dt} = +C\omega sin(\omega t) =\$ +ve from \$\omega t=0\$ to \$\pi/2\$ and the diode turns out to be forward biased.
However we know the diode is indeed reverse biased, but where did my math go wrong?