证明 1 arctan(1/5)+arctan(2/3)=派/4 2 aectan(3/4)=2arctan(1/2)

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证明 1 arctan(1/5)+arctan(2/3)=派/4 2 aectan(3/4)=2arctan(1/2)
证明 1 arctan(1/5)+arctan(2/3)=派/4 2 aectan(3/4)=2arctan(1/2)

证明 1 arctan(1/5)+arctan(2/3)=派/4 2 aectan(3/4)=2arctan(1/2)
1
arctan(1/5)+arctan(2/3)=派/4
设arctan(1/5)=X arctan(2/3)=Y
∵tan﹙X+Y﹚=﹙tanX+tanY﹚/﹙1﹣tanXtanY﹚=﹙1/5+2/3﹚/﹙1-1/5×2/3﹚=1
而tan派/4=1
∴arctan(1/5)+arctan(2/3)=派/4
2
aectan(3/4)=2arctan(1/2)
aectan(3/4)=X arctan(1/2)=Y
∵tanX=3/4
tan2Y=﹙2tanY﹚/﹙1-tan²Y﹚=﹙2×1/2﹚/﹙1-1/4﹚=4/3
是不是
aectan(3/4)=2arctan(1/2) “3/4”有误?应该为 "4/3"