In this paper by using the symplectic transformation condition, some new formulas including Chebyshev Polynomial, trigonometric identity, hyperbolic identity were obtained.

利用辛变换条件得到了一些新的切比雪夫多项式公式、三角恒等式和双曲恒等式。

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The author explores the solution to the best time problem according to three ways of thinking, including basic trigonometric identity, geometrical optics of physics and Geometer's Sketchpad.

利用基本三角恒等式、物理学中几何光学知识和几何画板软件等三种思维方法，来探讨一个最短时间问题的解法。

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