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Question

Let α=π3 then the solution set of the inequality logsinα(2cos2x)<logsinα(1sinx) where xϵ(0,2π) and xπ2 is

A
(α,πα)
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B
(α,π2)(π2,πα)
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C
(π3,5π6)
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D
(0,π2)(π2,π)
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Solution

The correct option is D (0,π2)(π2,π)
logsinα(2cos2x)logsinα(1sinx)<0logsinα(2cos2x1sinx)<0sin(π3)=32<1,log10[2cos2x1sinx]>0Gives,2cos2x1sinx>11+sin2x>1sinxsinx(1+sinx)>0sinx(0,1)x(0,π2)(π2,π)

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