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The equation 2cos^2(x/2)sin^2x=x^2+x^(-2...

The equation `2cos^2(x/2)sin^2x=x^2+x^(-2);0 <= x <=pi/2` has

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`(2cos^2x/2)sin^2x=x^2+1/x^2`
LHS
`0ltxltpi/2`
`cos0>cosx>=cospi/2`
`1>cosx>=0`
`2>1+cosx>=1`
`1<1+cosx<2`
`-1<=sinx<=1`
...
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