SOLUTION: solve for x in the equation: arc tan (x+1)+arc tan (x-1)=arc tan (12)

Question 770305: solve for x in the equation: arc tan (x+1)+arc tan (x-1)=arc tan (12)
Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
solve for x in the equation: arc tan (x+1)+arc tan (x-1)=arc tan (12)
***
let angle A=arc tan (x+1)
let angle B=arc tan (x-1)
let angle C=arc tan (12)
A+B=C
tan(A+B)=tan(C)
..
Identity: tan(A+B)=(tanA+tanB)/(1-tanA*tanB)
(x+1+x-1)/(1-(x+1)(x-1))=2x/1-x^2+1=2x/(2-x^2)
tan(A+B)=tan(C)
2x/(2-x^2)=12
2x=24-12x^2
12x^2+2x-24=0
6x^2+x-12=0
(2x+3)(3x-4)=0
x=-3/2
or
x=4/3

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