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Question
If `tan^-1x + tan^-1y = pi/4`, then ______
Options
x + y + xy = 1
x + y - xy = 1
x + y + xy + 1 = 0
x + y - xy + 1 = 0
MCQ
Fill in the Blanks
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Solution
If `tan^-1x + tan^-1y = pi/4`, then x + y + xy = 1.
Explanation:
Given, `tan^-1x + tan^-1y = pi/4`
⇒ `tan^-1((x + y)/(1 - xy)) = tan^-1`
⇒ `(x + y)/(1 - xy) = 1 ⇒ x + y + xy = 1`
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Derivative of Inverse Functions
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