Firstly, it is clear that the maximum value of W is the maximum value of horizontal resultant force Fx required when the displacement S is determined.
Through the stress analysis diagram, you can write:
f 1 = F2 = umg；
FX = f 1+F2 * cosa-u(mg-F2 * Sina)
=F 1(cosa+usina)
= radical sign (1+u 2) * f1* sin (a+b)
B=arctanu, when a+b=90 degrees, that is, a=arcctgu, the maximum value obtained by this trigonometric function is F 1* root sign (1+μ 2), and the maximum value of w is s*F 1* root sign (1).
You asked me why after Fx=F 1(cosa+usina) = root sign (1+U 2) * F 1 * SIN (A+B). This is the formula of trigonometric function, which was studied in mathematics in the first semester of senior high school, but it was used in the physical mechanics part of senior high school last semester, but it doesn't matter if you remember it or not.
B is arctanu, which is usually written for the convenience of expression. A is the included angle between F 1 and F2. This trigonometric function takes a as the independent variable, that is, when finding how much a is, the function gets the maximum value. This is an extreme value problem of trigonometric function, which will be learned in mathematics in the future.