Prove that arctan (2+sqrt3)+arctan (2-sqrt3)=pi/2 Solution Let us assume that:\\ arctan (2+ sqrt3) = x arcttan (2-sqrt3) = y ==> tanx = 2+ sqrt3 ==> tany = 2-sqrt3 Now we know that: tan (x+y) = (tanx + tany)/[1- tanx*tany] ==> tan (arctan (2+ sqrt3) + arctan(2-sqrt3) = tan (x+y) = (2+sqrt + 2-sqrt3)/ (1- (2+sqrt3)(2-sqrt3) = 4/ 1- 1 = 4/0= inf ==> tan[arcttan (2+sqrt3) + arctan (2-sqrt3) ]= infinity ==> arcttan( 2+sqrt3) + arctan (2-sqrt3) = pi/2.