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For x,yepsilonR with 0 lt x lt (pi)/2 such that ((sinx)^(2y))/((cosx)^((y^(2))/2))+((cosx)^(2y))/((sinx)^((y^(2))/2))=sin2x, then y is ________. |
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Answer» `((SINX)^(2y))/((cosx)^((y^(2))/2))+((cosx)^(2y))/((sinx)^((y^(2))/2))=2(sinx.cosx)^(y-(y^(2))/4)` It follows that `sin 2x ge 2(sinx.cosx)^(y-(y^(2))/4)` `:' sin x .COS XLT 1implies1 le y - (y^(2))/4` or `(1-(y^(2))/2)^(2) le 0` `impliesy=2` and `sin=cosx` So there is a unique solution `x-(pi)/4, y=2` |
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