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Question

The value of x in the interval [0,2π] for which 4sin2x8sinx+30 is

A
[π6,π2]
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B
[π3,π2]
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C
[π6,3π2]
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D
[π6,5π6]
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Solution

The correct option is D [π6,5π6]
4sin2x8sinx+30(2sinx1)(2sinx3)0
As 2sinx<3, so for the inequality to be true,
sinx12
So, from the graph


x[π6,5π6]

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