How do you find the exact value of arctan((arctan(9/7) - arctan(7/6)) / (arctan(5/3) - arctan(3/2)))?

1 Answer
Sep 9, 2015

Answer:

Find arctan

Explanation:

#tan x = 9/7# --> arc x = 52.15 deg
#tan y = 7/6# --> arc y = 49.39 deg
arc x - arc y = 52.19 - 49.39 = 2.73 deg
#tan u = 5/3# --> arc u = 59.03 deg
#tan v = 3/2# --> arc v = 56.30 deg
arc v - arc u = 59.03 - 56.30 = 2.73

#(arc x - arc y)/(arc u - arc v) = 2.73/2.73 = 1#.

#tan A = (arctan (9/7) - arctan (7/6))/(arctan (5/3) - arctan (3/2)) = 1 #--> #arc A = pi/4#