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Question

If tan−1(x+1)+tan−1(x−1)=tan−1(831), then x is equal to:

A
12
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B
12
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C
14
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D
1
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Solution

The correct option is A 12
tan1(x+1)+tan1(x1)

=tan1(x+1+x1)1(x+1)(x1)

=tan1(2x1(x21))

=tan1(2x2x2)=tan1(47)

2x2x2=47

14x=84x2

4x2+14x8=0

2x2+7x4=0

2x2+8xx4=0

2x(x+4)1(x+4)=0

x=4 OR x=12

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