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𝐷𝑖𝑓𝑓𝑒𝑟𝑒𝑛𝑡𝑖𝑎𝑡𝑒 𝑤𝑖𝑡ℎ 𝑟𝑒𝑠𝑝𝑒𝑐𝑡 𝑡𝑜 𝑥, 𝑦=arccos⁡((1−𝑥^2)/(1+𝑥^2 ))

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𝑆ℎ𝑜𝑤 𝑡ℎ𝑎𝑡 𝑑/𝑑𝜃 (2𝑎𝑟𝑐𝑡𝑎𝑛𝜃)=𝑑/𝑑𝜃 [arctan⁡(2𝜃/(1−𝜃^2 )) ]. 𝑊ℎ𝑦 𝑎𝑟𝑒 𝑡ℎ𝑒 𝑡𝑤𝑜 𝑟𝑒𝑠𝑢𝑙𝑡𝑠 𝑒𝑞𝑢𝑎𝑙