How do you prove that ArcTan(1) + ArcTan(2) + ArcTan(3) = π?
1 Answer
Sep 24, 2015
Prove that (arctan (1) + arctan (2) + arctan (3) = pi)
Explanation:
Call artan (1) = x; arctan (2) = y; and arctan (3) = z
Apply the trig identity:
First evaluate tan u = tan (x + y);
Next, evaluate tan (z + u)
Finally: tan (u + z) = tan (x + y + z) = 0 =
arctan (1) + arctan (2) + arctan (3) = x + y + z =