1.

-atan(1/239) %2B 4*atan(1/5)=pi/4

Answer»

let x = arctan Atan x = Atan (x + x) = (tan x + tan x)/(1 - tan x . tan x)tan 2x = (2 tan x) / (1 - tan^2 x)tan 2x = (2A) / (1 - A^2)2x = arctan ((2A) / (1 - A^2))2 arctan A = arctan ((2A) / (1 - A^2))4 arctan A = 2 arctan ((2A) / (1 - A^2))4 arctan (1/5) = 2 arctan ((2.1/5) / (1 - 1/25))= 2 arctan (5/12)= 2 arctan (5/12) - arctan (1/239)= arctan ((2.5/12) / (1 - 25/144)) - arctan (1/239)= arctan (120/119) - arctan (1/239)= arctan ((120/119 - 1/239) / (1 + 120/119 * 1/239)= arctan (1.0042 / 1.0042)= arctan (1)= π/4


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