Trigonometric Functions (please help)

Question

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302

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

Guest Jul 9, 2022

Guest · Answer 1 · 2022-07-09T10:21:18

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xy + x + y = sqrt(2).

Guest Jul 9, 2022

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that's wrong

Guest Jul 9, 2022

+50

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Can you explain how you now? Or your cheating on homework?

BigBrain Jul 10, 2022

CPhill · Answer 2 · 2022-07-09T11:31:01

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

Guest · Answer 3 · 2022-07-10T11:10:22

Using the trig identity

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

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