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Question

Find x, if x(0,1)
3sin1(2x1+x2)4cos1(1x21+x2)+2tan1(2x1x2)=π3

A
13
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B
13
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C
23
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D
23
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Solution

The correct option is A 13
Put x=tanθ
tan1x=θ(0,π4)2θ(0,π2)
Now,
3sin1(2tanθ1+tan2θ)4cos1(1tan2θ1+tan2θ)+2tan1(2tanθ1tan2θ)=π33sin1(sin2θ)4cos1(cos2θ)+2tan1(tan2θ)=π3
Since we know that 2θ(0,π2), the above expression can be written as
32θ42θ+22θ=π32θ=π3θ=π6x=tanπ6=13

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