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

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

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Answer 1 · 2015-09-09T23:21:56

Find arctan

Explanation:

$tan x = \frac{9}{7}$ $tan x = 9/7$ --> arc x = 52.15 deg
$tan y = \frac{7}{6}$ $tan y = 7/6$ --> arc y = 49.39 deg
arc x - arc y = 52.19 - 49.39 = 2.73 deg
$tan u = \frac{5}{3}$ $tan u = 5/3$ --> arc u = 59.03 deg
$tan v = \frac{3}{2}$ $tan v = 3/2$ --> arc v = 56.30 deg
arc v - arc u = 59.03 - 56.30 = 2.73

$\frac{a r c x - a r c y}{a r c u - a r c v} = \frac{2.73}{2.73} = 1$ $(arc x - arc y)/(arc u - arc v) = 2.73/2.73 = 1$ .

$tan A = \frac{arctan (\frac{9}{7}) - arctan (\frac{7}{6})}{arctan (\frac{5}{3}) - arctan (\frac{3}{2})} = 1$ $tan A = (arctan (9/7) - arctan (7/6))/(arctan (5/3) - arctan (3/2)) = 1$ --> $a r c A = \frac{π}{4}$ $arc A = pi/4$

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

1 Answer

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