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Question

If 4sin2x8sinx+30,0x2π,xϵ

A
[0,π6]
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B
[0,5π6]
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C
[5π6,2π]
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D
[π6,5π6]
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Solution

The correct option is D [π6,5π6]
4sin2x8sinx+30

4sin2x6sinx2sinx+30

2sinx(2sinx3)1(2sinx3)0

2sinx3=0,2sinx1=0

sinx=32,sinx=12

sinx32 since it is not in range of sinx

sinx=12

x=π6

sinx=sinπ6=12

sinx=sin(ππ6)=12

x[π6,ππ6]=[π6,5π6]


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