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Question Number 68782 by Maclaurin Stickker last updated on 06/Oct/19

$$\mathrm{Let}{d}_n\mathrm{be}\mathrm{the}\mathrm{determinant}\mathrm{of}\mathrm{the}n\times n$$$$\mathrm{matrix}\mathrm{whose}\mathrm{entries},\mathrm{from}\mathrm{left}\mathrm{to}\mathrm{right}$$$$\mathrm{and}\mathrm{then}\mathrm{from}\mathrm{top}\mathrm{to}\mathrm{bottom},\mathrm{are}$$$$cos1,cos2,...,cos{n}^2.(\mathrm{For}\mathrm{example},$$$$d_3=\left|\begin{array}{c}cos1cos2cos3\\ cos4cos5cos6\\ cos7cos8cos9\end{array}\right|.$$$$\mathrm{The}\mathrm{argument}\mathrm{of}cos\mathrm{is}\mathrm{always}\mathrm{in}\mathrm{radians}$$$$\mathrm{not}\mathrm{degrees}.)$$$$\mathrm{Evalue}\underset{n\to \mathrm{\infty }}{\lim }{d}_{n.}$$

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