Introduction:
When a continuous-time signal is sampled at a certain frequency, the resulting discrete-time signal is obtained. In this case, we are given a continuous-time signal x(t) = cos(2*pi*40*t) and we need to determine the output signal when it is sampled with a sampling frequency of 20Hz.

Sampling:
Sampling is the process of converting a continuous-time signal into a discrete-time signal by taking samples at regular intervals. The sampling frequency is the number of samples taken per second. In this case, the sampling frequency is 20Hz, which means that 20 samples are taken per second.

Sampling Theorem:
According to the Nyquist-Shannon sampling theorem, in order to accurately reconstruct a continuous-time signal from its samples, the sampling frequency should be at least twice the maximum frequency component present in the signal. This is known as the Nyquist rate. In this case, the maximum frequency component of the signal x(t) is 40Hz, so the sampling frequency of 20Hz satisfies the Nyquist rate.

Discrete-Time Signal:
When the continuous-time signal x(t) is sampled with a sampling frequency of 20Hz, the resulting discrete-time signal can be written as x[n] = x(n*T), where T is the sampling period and n is an integer. The sampling period is the reciprocal of the sampling frequency, T = 1/20s.

Applying the Sampling Formula:
Substituting the values into the sampling formula, we get x[n] = cos(2*pi*40*(n*T)). Simplifying further, we have x[n] = cos(2*pi*40*(n*(1/20))). Canceling out the 40 and 20, we get x[n] = cos(4*pi*n).

Output Signal:
From the simplified expression, we can see that the output signal is x[n] = cos(4*pi*n). This means that the discrete-time signal obtained by sampling the continuous-time signal x(t) = cos(2*pi*40*t) with a sampling frequency of 20Hz is a cosine signal with a frequency of 4*pi.

Conclusion:
The correct answer is option 'C', cos(4*pi*n), which represents the output signal when the signal x(t) = cos(2*pi*40*t) is sampled with a sampling frequency of 20Hz.