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4tan^-1 (1/5) - tan^-1 (1/239)is equal toA) πB) π/2C) π/3D) π/4

4tan^-1 (1/5) - tan^-1 (1/239)is equal toA) πB) π/2C) π/3D) π/4

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1 Answers

Arun
25750 Points
5 years ago
let x = arctan A 
tan x = A 
tan (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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