reserve x,x0, r, s, h for Real,

  n for Element of NAT,
  rr, y for set,
  Z for open Subset of REAL,

  f, f1, f2 for PartFunc of REAL,REAL;

theorem Th42:
  cot.(PI/2) = 0 & cot (PI/2) = 0
proof
A1: PI/2 < PI/1 by XREAL_1:76;
A2: PI/2 in ].0,PI.[ by A1,XXREAL_1:4;
  then cot.(PI/2) = 0/sin.(PI/2) by Th2,RFUNCT_1:def 1,SIN_COS:76
    .= 0;
  hence thesis by A2,Th14;
end;
