4tan^-1 (1/5) - tan^-1 (1/239)is equal toA) πB) π/2C) π/3D) π/4
Technical GURUJI , 7 Years ago
Grade
Trigonometry> 4tan^-1 (1/5) - tan^-1 (1/239)is equal to...
1 Answers
Arun
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
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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