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tanπ/9+tan2π/9+根号3tanπ/9tan2π/9=?
题目详情
tanπ/9+tan2π/9+根号3tanπ/9tan2π/9=?
▼优质解答
答案和解析
tanπ/9+tan2π/9+√3tanπ/9tan2π/9
=tan(π/9+2π/9)(1-tanπ/9tan2π/9) +√3tanπ/9tan2π/9
=tanπ/3(1-tanπ/9tan2π/9) +√3tanπ/9tan2π/9
=√3(1-tanπ/9tan2π/9) +√3tanπ/9tan2π/9
=√3-√3tanπ/9tan2π/9 +√3tanπ/9tan2π/9
=√3
=tan(π/9+2π/9)(1-tanπ/9tan2π/9) +√3tanπ/9tan2π/9
=tanπ/3(1-tanπ/9tan2π/9) +√3tanπ/9tan2π/9
=√3(1-tanπ/9tan2π/9) +√3tanπ/9tan2π/9
=√3-√3tanπ/9tan2π/9 +√3tanπ/9tan2π/9
=√3
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