(tg(a) - ctg(a))/( sin(a) - cos(a) ) = ( (sin(a)/cos(a) ) - (cos(a)/sin(a)) ):
: (sin(a) - cos(a) ) = (sin²(a) - cos²(a))/( sin(a)*cos(a)*( sin(a)-cos(a) ) ) =
= (sin(a) - cos(a))*(sin(a)+cos(a))/(sin(a)*cos(a)*(sin(a)-cos(a))) =
= (sin(a)+cos(a))/(sin(a)*cos(a)) = V
sin(a) + cos(a) = 1,2
возведем последнее равенство в квадрат:
(sin(a)+cos(a))^2 = 1,2^2;
sin^2(a) + cos^2(a) + 2*sin(a)*cos(a) = 1,44,
используем основное триг-ое тождество:
sin^2(a)+cos^2(a) = 1, поэтому
1+2*sin(a)*cos(a) = 1,44,
2*sin(a)*cos(a) = 1,44 - 1 = 0,44;
sin(a)*cos(a) = 0,44/2 = 0,22;
поэтому
V = 1,2/(0,22) = 120/22 = 60/11