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Question

The number of solutions to the equation
tan1(x+1)+tan1x+tan1(x1)=πtan13 is :

A
1
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B
2
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C
3
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D
4
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Solution

The correct option is A 1
We have tan1(x+1)+tan1(x1)
=πtan13tan1x=π(tan13+tan1x)
Taking tan of both sides, we have
(x+1)+(x1)1(x+1)(x1)=3+x13x
2x6x2=(3+x)(x22)
x3+9x24x6=0
(x1)(x2+10x+6)=0
x=1orx=5±19
Clearly x = 1 satisfies the equation as
L.H.S = tan12+tan11+tan10=π+tan12+112
=πtan11=3=R.H.S.
While x=5±19 do not satisfy the equation.

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