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Question

If 3tan1x=tan1(3xx313x2), then x belongs to

A
[1,1]
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B
(1,1)
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C
[13,13]
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D
(,)
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Solution

The correct option is B (,)

Consider the given function

3tan1x=tan1(3xx313x2)

Let put x=tanθthenθ=tan1x we get,

3tan1tanθ=tan1(3tanθtan3θ13tan2θ)

3θ=tan1tan3θ

3θ=3θ

θ=θ


θ=tan1x

x=tanθ


We know that,

θ[π2,π2] then

x(,)


Hence,the answer is option D


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