Ngô Quốc Anh

October 3, 2007

1 đẳng thức liên quan đến hàm arctan

Filed under: Các Bài Tập Nhỏ — Ngô Quốc Anh @ 22:44

\tan^{-1}\,A+\tan^{-1}\,B+\tan^{-1}\,C=\tan^{-1}\left(\dfrac{A+B+C-ABC}{1-AB-BC-CA}\right)

Áp dụng. Với x\ne 0 ta luôn có

\boxed {\ \arctan x + \arctan \left(x^3\right) + \arctan\frac {1 - x^2}{x} = \frac {\pi}{2}\cdot\frac {|x|}{x}\ }\ .

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