求arctan(1/5)+arctan(2/3)答案为 派/4

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求arctan(1/5)+arctan(2/3)答案为 派/4

求arctan(1/5)+arctan(2/3)答案为 派/4
求arctan(1/5)+arctan(2/3)
答案为 派/4

求arctan(1/5)+arctan(2/3)答案为 派/4
求arctan(1/5)+arctan(2/3)
tan[arctan(1/5)+arctan(2/3)]=
=[tanarctan(1/5)+tanarctan(2/3)]/[1-tanarctan(1/5)tanarctan(2/3)]
=[(1/5)+(2/3)]/[1-(1/5)(2/3)]=(13/15)/(13/15)=1

令第一个等于a,第二个等于b
则tana=1/5,tanb=2/3
则00所以0tan(a+b)=(tana+tanb)/(1-tanatanb)=1
0所以a+b=π/4