求证arctan1/2+arctan1/5+arctan1/8=pai/4
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求证arctan1/2+arctan1/5+arctan1/8=pai/4求证arctan1/2+arctan1/5+arctan1/8=pai/4求证arctan1/2+arctan1/5+arct
求证arctan1/2+arctan1/5+arctan1/8=pai/4
求证arctan1/2+arctan1/5+arctan1/8=pai/4
求证arctan1/2+arctan1/5+arctan1/8=pai/4
问题等价于 若tana=1/2 tanb=1/5 tanc=1/8则a+b+c=π/4
证
tan(a+b)=(tana+tanb)/(1-tanatanb)=7/9
tan(a+b+c)=[tan(a+b)+tanc]/[1-tan(a+b)tanc]=1
因此a+b+c=arctan(1)=π/4
求证arctan1/2+arctan1/5+arctan1/8=pai/4
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arctan1/2+arctan1/5+arctan1/3
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