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Question

If tanāˆ’1(xāˆ’1)+tanāˆ’1(x+1)+tanāˆ’1x=tanāˆ’13x, then in the interval [āˆ’1,1], then x has :

A
one value
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B
2 values
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C
3 values
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D
No value
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Solution

The correct option is C 3 values
Given equation tan1(x1)+tan1(x+1)=tan13xtan1x
tan1(x1)+(x+1)1(x1)(x+1)=tan13xx1+3x.x
2x2x2=2x1+3x2
2x(4x21)=0x=0,±12
All three solutions satisfy the given equation.

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