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Question

The number of solution of the equation tan1(x1x2)+tan1(1x3)=3π4 belonging to the interval (0, 1) is


A

0

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B

1

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C

2

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D

3

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Solution

The correct option is A

0


xϵ(0,1)x1x2>0, 1x3>0&x1x2.1x3>1
tan1x1x2+tan11x3=π+tan1(x1x2+1x31x1x2.1x3)=π+tan1(1x)=3π4
x=1 (not possible)


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