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根据tan45°=tan(21°+24°)=
tan21°+tan24°
1-tan21°tan24° =1
得到tan21°+tan24°=1-tan21°tan24°①;同理得到tan22°+tan23°=1-tan22°tan23°②;
则原式=[(1+tan21°)(1+tan24°)][(1+tan22°)(1+tan23°)]
=(1+tan24°+tan21°+tan24°tan21°)(1+tan22°+tan23°+tan22°tan23°)
=(1+1-tan24°tan21°+tan24°tan21°)(1+1-tan22°tan23°+tan22°tan23°)=4
故答案为:4.
1年前
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