It is claimed that this formula: Pi/4=4 arctan(1/5) - arctan(1/239) is derived from the following 2 formulas:

Sin(a+B)=sin(a)cos(B)+cos(a)sin(B)..........(1)

Cos(a+B)=cos(a)cos(B)-sin(a)sin(B)..........(2)

My question is: How, and what are the steps involved? Any insights will be appreciated. Thank you.

Guest Jul 13, 2017

#1**+1 **

This formula: pi/4=4arctan(1/5) - arctan(1/239) is called "Machin's formula", after the Scottish mathematician John Machin. It is used to calculate Pi to as many digits as you want and it is very efficient. It is true that it is derived from 2 "angle addition" equations you cited. You can see the derivation here, if you can follow it:

https://en.wikipedia.org/wiki/Machin-like_formula

Guest Jul 13, 2017