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The equation 2 "cos"^(2)((x)/(2))"sin"^(...

The equation `2 "cos"^(2)((x)/(2))"sin"^(2) x = x^(2) + (1)/(x^(2)), 0 le x le (pi)/(2)` has

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The given equation is
`2 cos^(2) (x/2) sin^(2) x=x^(2) +1/x^(2)`
where `0 lt x le pi/2`
`LHS=2 cos^(2) (x/2) sin^(2) x=(1+cos x) sin^(2)x`
`:' 1+cos x lt 2 and sin^(2) x le 1` for `0 lt x lt pi/2`
`:. (1+ cos x) sin^(2) x lt 2`
Also, `R.H.S.=x^(2) +1/x^(2) ge 2`
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