If a+B+y= pie, shwo that tan a+tan B+ tan y= tan a tan B tan y

If a+B+y= pie, shwo that tan a+tan B+ tan y= tan a tan B tan y
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tan(y)=tan(π-(a+B))=-tan(a+B), so tan(a)+tan(B)+tan(y)=tan(a)+tan(B)-tan(a+B).

tan(y)=-tan(a+B)=-(tan(a)+tan(B))/(1-tan(a)tan(B)),

tan(y)-tan(y)tan(a)tan(B)=-(tan(a)+tan(B)),

tan(y)+(tan(a)+tan(B))=tan(y)tan(a)tan(B), which is the same as:

tan(a)+tan(B)+tan(y)=tan(a)tan(B)tan(y) QED
by Top Rated User (1.2m points)

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