已知tan(a+b)=1⼀2,tan(a-45°)=-1⼀3,求tan(b+45°)的值得

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2025-04-28 22:44:41
推荐回答(3个)
回答1:

tan(b+45)=tan[(a+b)-(a-45)]
=[tan(a+b)-tan(a-45)]/[1+tan(a+b)tan(a-45)]
=(1/2+1/3)/(1-1/2*1/3)
=1

回答2:

a+b=a-45°+b+45°
tan(a+b)=[tan(a-45°)+tan(b+45°)]/[1-tan(a-45°)tan(b+45°)]=1/2
[-1/3+tan(b+45°)]/[1+tan(b+45°)/3]=1/2
-1/3+tan(b+45°)=1/2+tan(b+45°)/6
5/6tan(b+45°)=5/6
tan(b+45°)=1

回答3:

tan(b+45)=tan(( a+b)-(a-45))=(tam(a+b)-tan(a-45))/(1-tan(a+b)*tan(a-45))
=(1/2+1/3)/(1+5/6)=5/11