证明恒等式arctanx+arccotx=π/2 , f(x) = arctanx+arccotx, 则有f'(x) = 1/(1 + x^2) - 1/(1 + x^2) = 0,f(x) = arctanx+arccotx,则有f'(x) = 1/(1 + x^2) - 1/(1 + x^2) = 0,所以由那个定理,f(x)是常数.把x = 1代入,得到f(1) = arctan 1 + a
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那个f'(x)就相当于导数,倒数为零就意味着f(x)的图像为一条水平线,即f(x)为一常数,所以无论是谁都得TT/2