why there is -ve sign in the phase shift of RL low pass filter?
For an inductor, the basic relationship between voltage and current is: -

V = L di/dt

Or, put another way, the rate of change of current (with respect to time) determines how big the voltage will be.

We can mathematically integrate both sides and we see that the time-integral of the applied voltage is proportional to current. So, if the input voltage is a sinewave, it's time integral is a negative cosine wave: -



For the low pass filter, as frequency rises, the inductive reactance becomes more dominant (despite the presence of the resistor) and the output magnitude begins to noticeably fall as the frequency gets close to and advances past the -3 dB point: -



Ultimately, at a high enough frequency, the phase angle of the current through the resistor is dominated by the inductive reactance. In other words, XL has become very large with respect to R. This means that the phase angle of the output voltage starts at zero degrees (low frequencies) and ends up at -90 degrees (high frequencies).

E.g. if XL has risen to 1000 and R is 1 then arctan of -1000 is -89.94 degrees.