simplifying inverse tan (1 Viewer)

[tacogym27101990]

how would you simplify something like atan(2) - atan(0.5)???
do the same laws as logs apply??

thanks

 

[undalay]

x = atan(2) - atan(0.5)

let arctan 2 = a
arc tan 0.5 = b

tan x = tan (a-b)
tan x= ( a-b )/1+tanaxtanb
tan x= 3/4
x = arctan 3/4

thus atan(2) - atan(0.5) = aarctan 3/4

 

[Trebla]

Prove the relevant theorem:
Let x = atan 2 => 2 = tan x
and y = atan 0.5 => 0.5 = tan y
tan (x - y) = [tan x - tan y]/[1 + tan x.tan y]
= [2 - 0.5]/[1 + (2)(0.5)]
= 3/4
.: x - y = atan 0.75
i.e. atan 2 - atan 0.5 = atan 0.75

 

[tacogym27101990]

oo thats kinda cool
thanks