证明恒等式arctanx+arccotx=π/2
问题描述:
证明恒等式arctanx+arccotx=π/2
答
令 α = arctan x,则 cot (π/2 - α) = tan α = x
由于 α∈]-π/2,π/2[,故 π/2 - α∈]0,π[
这样 arccot x = π/2 - α,即 arctan x + arccot x = π/2