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)
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"
再问: 是的是的 我打错了 应该是4/3
再答: 2 aectan(4/3)=2arctan(1/2) 设aectan(4/3)=X arctan(1/2)=Y ∵tanX=4/3 tan2Y=﹙2tanY﹚/﹙1-tan²Y﹚=﹙2×1/2﹚/﹙1-1/4﹚=4/3 ∴aectan(4/3)=2arctan(1/2)
再问: tan2y=2tany??
再答: ∵tan﹙m+n﹚=﹙tan m+tan n﹚/﹙1-<tan m><tan n>﹚ ∴ 当m=n=Y时 tan2Y=﹙2tanY﹚/﹙1-tan²Y﹚
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"
再问: 是的是的 我打错了 应该是4/3
再答: 2 aectan(4/3)=2arctan(1/2) 设aectan(4/3)=X arctan(1/2)=Y ∵tanX=4/3 tan2Y=﹙2tanY﹚/﹙1-tan²Y﹚=﹙2×1/2﹚/﹙1-1/4﹚=4/3 ∴aectan(4/3)=2arctan(1/2)
再问: tan2y=2tany??
再答: ∵tan﹙m+n﹚=﹙tan m+tan n﹚/﹙1-<tan m><tan n>﹚ ∴ 当m=n=Y时 tan2Y=﹙2tanY﹚/﹙1-tan²Y﹚
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