If A+B = 225 then what would be (1+tan A)(1+tan B) = ??

Question

Try to solve this problem using substitution of only basic values of trigonometric functions(30,60,90) and post the complete solution?

Answer 1

A+B=225;; A+B=180+45 ;; -45=180-(A+B)  ;;

TAKING TAN BOTH SIDES ;;; TAN(-45)=TAN(180-(A+B));;; -1=-TAN(A+B);;

                  TAN(A+B)=1 ;;;
                  TAN(A) + TAN(B) = 1- TAN(A)TAN(B) ;;;
                  TAN(A)+TAN(B)+TAN(A)TAN(B) = 1 ;;


       Question was to find {1+TAN(A)}{1+TAN(B)} === 1+ TAN(A) +TAN(B) + TAN(A)TAN(B)  == 1+ 1 == 2

Answer 2