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The equation `2sin^(2)((x)/(2))cos^(2)x=x+(1)/(x),0 lt x le(pi)/(2)` hasA. one real solutionB. no real solutionC. infinitely many real solutionsD. None of these |
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Answer» Correct Answer - B We know that `2"sin"^(2)(x)/(2)cosxle2` and `x+(1)/(2)ge2` for `0 lt x lt (pi)/(2)` Thus, `2"sin"^(2)(x)/(2)cosx=x,x+(1)/(2)` holds good only when each side is eaul to 2. We observe that `x+(1)/(x)=2` for x=1 only. But, `2"sin"^(2)(x)/(2) cos x ne 2` for x=1. Hence, the given equation has no real solution. |
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