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Question

The range of x for which the formula 3sin1x=sin1[x(34x2)] hold is

A
12x12
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B
14x23
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C
13x1
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D
23x23
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Solution

The correct option is A 12x12
Given : 3sin1x=sin1[x(34x2)]....(i)
Let sin1x=θ
x=sinθ....(ii)
Now, from Eq (i)
3θ=sin1[sinθ(34sin2θ)]
Here, π23θπ2
[ sin1x is in the interval [π2,π2]
π6θπ6
12sinθ12
x=sinθ
12x12

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