tan(x)*tan(c-x)=1.谁能帮我解释下.对于任意的x属于(0,PI/2),存在常数c使得,tan(x)*tan(c-x)=1.我的论证如下:因为由(-1)/(1+x^2)的不定积分可得两种表达方式:1.arctan(1/x)+c0;(做恒等变
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![tan(x)*tan(c-x)=1.谁能帮我解释下.对于任意的x属于(0,PI/2),存在常数c使得,tan(x)*tan(c-x)=1.我的论证如下:因为由(-1)/(1+x^2)的不定积分可得两种表达方式:1.arctan(1/x)+c0;(做恒等变](/uploads/image/z/1804221-45-1.jpg?t=tan%EF%BC%88x%EF%BC%89%2Atan%EF%BC%88c-x%EF%BC%89%3D1.%E8%B0%81%E8%83%BD%E5%B8%AE%E6%88%91%E8%A7%A3%E9%87%8A%E4%B8%8B.%E5%AF%B9%E4%BA%8E%E4%BB%BB%E6%84%8F%E7%9A%84x%E5%B1%9E%E4%BA%8E%EF%BC%880%2CPI%2F2%EF%BC%89%2C%E5%AD%98%E5%9C%A8%E5%B8%B8%E6%95%B0c%E4%BD%BF%E5%BE%97%2Ctan%EF%BC%88x%EF%BC%89%2Atan%EF%BC%88c-x%EF%BC%89%3D1.%E6%88%91%E7%9A%84%E8%AE%BA%E8%AF%81%E5%A6%82%E4%B8%8B%EF%BC%9A%E5%9B%A0%E4%B8%BA%E7%94%B1%EF%BC%88-1%EF%BC%89%2F%281%2Bx%5E2%29%E7%9A%84%E4%B8%8D%E5%AE%9A%E7%A7%AF%E5%88%86%E5%8F%AF%E5%BE%97%E4%B8%A4%E7%A7%8D%E8%A1%A8%E8%BE%BE%E6%96%B9%E5%BC%8F%EF%BC%9A1.arctan%EF%BC%881%2Fx%29%2Bc0%3B%28%E5%81%9A%E6%81%92%E7%AD%89%E5%8F%98)
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