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Question

If α,β, and γ are the roots of tan1x+tan1(x+1)=tan13x, then

A
α+β+γ=0
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B
αβ+βγ+γα=1/3
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C
αβγ=1
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D
|αβ|max=1
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Solution

The correct option is D αβ+βγ+γα=1/3
tan1(x)+tan1(x+1)=tan1(3x)
tan1(2x+11x2x)=tan13x
Therefore after taking tan on both the sides, we get
2x+1=3x(1x2x)
2x+1=3x3x33x2
3x3+3x2x+1=0
αβ+βγ+γα=13

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