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阿Q吧 > 为什么(arccosx)✀=(π⼀2-arcsinx)✀

为什么(arccosx)✀=(π⼀2-arcsinx)✀

2025-03-16 13:25:10

推荐回答（2个）

回答1：

如图

回答2：

arcsinx+arccosx=π/2 ∵sin(arcsinx)=x sin(π/2-arccosx)=cos(arccosx)=x ∴sin(arcsinx)= sin(π/2-arccosx) 又arcsinx∈[-π/2,π/2] π/2-arccosx∈[-π/2,π/2] ∴arcsinx=π/2-arccosx ∴ arcsinx+arccosx=π/2

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