why is the voltage zero across the resistors in this circuit?
The answer is, it is, and it isn't.

You have missed one critical piece of information in your question, when. At steady-state, or during the transient period when the voltage is first applied.

It seems you added the information in the comments. It is fully charged, i.e. steady-state condition.



In the transient the capacitor will charge up through the resistors until it reaches \$1\mathrm{V}\$. Once the capacitor has reached this voltage (i.e. it is fully charged), assuming it is ideal and the voltage source remains constant, then you will have:

$$V_s=V_c$$

Clearly that means all the voltage is dropped across the capacitor, so there cannot be any voltage across the resistors.



For completeness, we can look at the steady state condition in another way. The reactance of a capacitor (similar to resistance, but frequency dependent), is given by:

$$X_c = \frac{1}{2\pi fC}$$

Where \$f\$ is the frequency, and \$C\$ is the capacitance. At DC, the frequency is \$0\mathrm{Hz}\$, so the reactance is:

$$X_c = \frac{1}{2\pi C\times 0} = \frac{1}{0} = ∞$$

So what will the current be if the reactance is infinite? \$I=\frac{V}{X_c}=0\$. If there is no current flowing, there can be no voltage across the resistors \$V=IR=0\times R=0\$.