constant independent of time, meaning of this line?
In the first case (where \$x_1(t)\$ and \$x_2(t)\$ are two sinusoidal signals that differ only in amplitude but not in frequency or phase angle) the quotient
\$\frac{x_1(t)}{x_2(t)}\$ is a constant. I.e. the quotient is the same at any time.
In the second case (where \$x_1(t)\$ and \$x_2(t)\$ are two sinusoidal signals that differ only in phase offset but not in amplitude or frequency) the quotient
\$\frac{x_1(t)}{x_2(t)}\$ is a not constant. I.e. the quotient is a function of time; it changes over time. In general it is not equal at two different times.


The expressions "constant independent of time" means that only dependence with respect to time is considered here. In other cases it might be interesting to consider dependency of other quantities, e.g. of frequency or space.