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If Pi/4 = 8Arctan(1/10) - Arctan(a/b), what is the fraction a/b? Thanks for help.

 Dec 20, 2020
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Arctan(a/b) =8arctan(1/10) - Pi/4


Arctan(a/b) =0.01195105653184790941190811320429


a/b =tan(0.01195105653184790941190811320429)


a/b =0.01195162554520335317930497716049


Using "continued fraction" method,  will convert the above decimal into a proper fraction, a/b:

 

About half a dozen elementary steps later, we get the proper fraction:


a / b == 1758719 / 147153121

 Dec 21, 2020

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