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If \(\tan^{-1} x + \tan^{-1} y = \frac{\pi}{4}, \) then compute \(xy + x + y. \)

 Jul 9, 2022
 #1
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xy + x + y = sqrt(2).

 Jul 9, 2022
 #2
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that's wrong

Guest Jul 9, 2022
 #5
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Can you explain how you now? Or your cheating on homework?indecision

BigBrain  Jul 10, 2022
 #3
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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

 

 

cool cool cool

 Jul 9, 2022
 #4
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Using the trig identity

 \(\displaystyle \tan(A+B)= \frac{\tan A + \tan B}{1- \tan A \tan B},\)

 

\(\displaystyle \tan(\tan^{-1}x+\tan^{-1}y)=\tan(\pi/4), \\ (x+y)/(1-xy)=1, \\x+y=1-xy, \\ x+y+xy=1.\)

 Jul 10, 2022

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