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The number of pairs (x, y) of real numbe...

The number of pairs (x, y) of real numbers with `0 lt x lt (pi)/( 2) " that " ((sin x)^(2y))/((cos x)^((y^(2))/(2)))+((cos x)^(2y))/((sin x) ^((y^(2))/(2)))= sin 2 x ` is equal to

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