Let (pi -2x) =y then 2x= (pi-y) and lim x tends to pi /2 can be written as lim y--0
lim y---0 (1+cos(pi-y) )/y2
= lim y---0 (1-cos y )/y2 ------------As cos(pi-x) = -cosx--------------
= lim y--0 (-2sin2(y/2) /y2 ---------------As cosy = 1-2sin2(y/2)-------
= -1/2 lim y--0 [(sin(y/ 2 )/(y/2)] 2 =-1/2 ------------Multiplyin by 4 to numerator and denominator--------