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Question
A solution of the equation tan-1(1 + x) + tan-1(1 - x) = `pi/2` is ______
Options
x = 1
x = -1
x = 0
x = π
MCQ
Fill in the Blanks
Solution
A solution of the equation tan-1(1 + x) + tan-1(1 - x) = `pi/2` is x = 0.
Explanation:
tan-1(1 + x) + tan-1(1 - x) = `pi/2`
⇒ `tan^-1(1 + x) = pi/2 - tan^-1(1 - x)`
⇒ `tan^-1(1 + x) = cot^-1(1 - x)`
⇒ `tan^-1(1 + x) = tan^-1(1/(1 - x))`
⇒ `1 + x = 1/(1 - x) ⇒ 1 - x^2 = 1 ⇒ x = 0`
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Solution of a Differential Equation
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