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Question Number 95598 by bagjamath last updated on 26/May/20

If  sin^(−1) x_1 +sin^(−1) x_2 +...+sin^(−1) x_(2n) =nπ,  then   Σ^(2n) _(i, j=1_(i ≠ j) )    x_i  x_j  =

$$\mathrm{If}\:\:\mathrm{sin}^{−\mathrm{1}} {x}_{\mathrm{1}} +\mathrm{sin}^{−\mathrm{1}} {x}_{\mathrm{2}} +...+\mathrm{sin}^{−\mathrm{1}} {x}_{\mathrm{2}{n}} ={n}\pi, \\ $$$$\mathrm{then}\:\:\:\underset{\underset{{i}\:\neq\:{j}} {{i},\:{j}=\mathrm{1}}} {\overset{\mathrm{2}{n}} {\sum}}\:\:\:{x}_{{i}} \:{x}_{{j}} \:= \\ $$

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