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Question

The set of all x in the interval [0,π] for which 2sin2x3sinx+10 is___


Solution

We have 2sin2x3sinx+10
or (2sinx1)(sinx1)0
or (sinx12)(sinx1)0
or sinx12orsinx1
But we know that sinx1 and sinx0 for x[0,π]..
Therefore, either sin x =1 or 0sinx12

eitherx=π2 or x[0,π6][5π6,π]
Combining, we get x[0,π6]{π2}[5π6,π].

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