If tan(x+y)=tanx+tany , what is tanxtany ?
tan(x+y)=(tanx+tany)/(1-tanxtany)
but given tan(x+y)=tanx+tany
so tan(x+y)=tan(x+y)/(1-tanxtany)
or (1-tanxtany)=tan(x+y)/tan(x+y)
or (1-tanxtany)=1
or -tanxtany=0
or tanxtany=0
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