Question

正切定理如何证明?谢拉!就是a+b/a-b那个...

Answer 1

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1...(a+b)/(a-b)=(sinA+sinB)/(sinA-sinB)

2...sinA+sinB=sin[(A+B)/2+(A-B)/2]+sin[(A+B)/2-(A-B)/2]=2sin[(A+B)/2]*cos[(A-B)/2]

3...sinA-sinB=sin[(A+B)/2+(A-B)/2]-sin[(A+B)/2-(A-B)/2]=2sin[(A-B)/2]*cos[(A+B)/2]

所以(a+b)/(a-b)=tg[(A+B)/2]/tg[(A-B)/2]