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Question

The interval for x which satisfies the equation 2tan12x=sin14x1+4x2 is

A
[12,)
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B
(,12]
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C
[1,1]
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D
[12,12]
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Solution

The correct option is D [12,12]
Given : 2tan12x=sin14x1+4x2
Let y=4x1+4x2
4yx24x+y=0xRD01616y20y210y[1,1]

So,
sin14x1+4x2[π2,π2]
The above equality is possible only when,
π22tan12xπ2π4tan12xπ412x112x12

Hence, the required values of x is
x[12,12]

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