If \(\tan^{-1} x + \tan^{-1} y = \frac{\pi}{4}, \) then compute \(xy + x + y. \)
xy + x + y = sqrt(2).
that's wrong
Can you explain how you now? Or your cheating on homework?
arctan x + arctan y = pi / 4
This will be true when either
x = 0 and y = 1
or
x = 1 and y = 0
So
xy + x + y = 1
Using the trig identity
\(\displaystyle \tan(A+B)= \frac{\tan A + \tan B}{1- \tan A \tan B},\)
\(\displaystyle \tan(\tan^{-1}x+\tan^{-1}y)=\tan(\pi/4), \\ (x+y)/(1-xy)=1, \\x+y=1-xy, \\ x+y+xy=1.\)
