# Trig

posted by Mike

give the value of:
Tan(Arctan x+1/x-1+Arctan x-1/x)

1. Reiny

let arctan((x+1)/(x-1)) = A or tanA = (x+1)/(x-1)
let arctan((x-1)/x) = B or tanB = (x-1)/x

then Tan(Arctan x+1/x-1+Arctan x-1/x)
= tan(A+B)
= (tanA + tanB)/(1-tanAtanB)
= [ (x+1)/(x-1) + (x-1)/x ] / [1 - (x+1)/(x-1)(x-1)/x ]
= ....
= (2x^2 - x + 1)/(1-x)

check my algebra

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