PI in ].0,4.[ by SIN_COS:def 28;
then A1: PI > 0 by XXREAL_1:4;
then A2: PI / 2 < PI / 1 by XREAL_1:76;
PI / 2 > 0 / 2 by A1, XREAL_1:74;
then A3: PI / 2 in ].0,PI.[ by A2, XXREAL_1:4;
then cot . (PI / 2) = 0 / (sin . (PI / 2)) by Th2, RFUNCT_1:def 1, SIN_COS:76
.= 0 ;
hence ( cot . (PI / 2) = 0 & cot (PI / 2) = 0 ) by A3, Th14; :: thesis: verum