Question

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

Answer 1

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`