Question

how can you solve tan{arctan[(x+1)/(x-1)] + arctan [(x-1)/x]}

Answer 1

draw it.

Answer 2

I tried letting a=(x+1)/(x-1) and b= (x-1)/x

Answer 3

\[\tan [\tan^{-1}\frac{ x+1 }{ x-1 } +\tan^{-1} \frac{ x-1 }{ x }]\]

Answer 4

Hmmmm

Answer 5

I mean how do you solve it analytically?

Answer 6

drawing is a good way to analyze.

Answer 7

can I solve it as arctan a+arctanb = arctan a+b/1-ab ?

Answer 8

Is that a property you are given?

Answer 9

yes

Answer 10

you can also use angle addition property for tangent
\[\tan(a+b) = \frac{\tan a +\tan b}{1 - \tan a \tan b}\]

Answer 11

thanks!

Answer 12

I got it now