Fast way to show this identity: Just draw the medians to the hypotenuse and to one side in an isosceles right-angled triangle. Since AF : FD = 2 : 1 AE = EC , BD = AD, The proof is completed.
The trigonometric way: By putting tan A = X and tan B = Y in the sum formula, We can get the arc tangent formula: \
	Exercise 1. Can you use the diagram to show that : ? (Hint: Find a right angle and a suitable straight angle in the diagram) 2. Can you draw another red triangle in the same lattice which can demonstrate the same result in 1 ?