The function f(x) = x^(1/sqrt(1-x^2)) is monotonically increasing for 0 < x < 1, easily verified by taking the derivative. Since 0 < sin x < cos x < 1 for 0 < x < pi/4, f(sin x) < f(cos x). But f(sin x) = (sin x)^(1/cos x) and f(cos x) = (cos x)^(1/sin x). Raising both sides to the power (cos x.sin x), we get the desired result.

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