求tanπ/9+4sinπ/9的值
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原式=sin(π/9)/cos(π/9）+(4sinπ/9×cosπ/9)/cosπ/9
=[sinπ/9+2sin2π/9]/cosπ/9
=[sinπ/9+sin2π/9+sin2π/9]/cosπ/9
={2sin[（π/9+2π/9)/2]cos[(π/9-2π/9)/2+sin2π/9}/cosπ/9
=[cosπ/18+sin2π/9]/cosπ/9
=[sin(π/2-π/18)+sin2π/9]/cosπ/9
=2sin[(4π/9+2π/9)/2]cos[(4π/9-2π/9)/2]/cosπ/9
=[2sinπ/3cosπ/9]/cosπ/9
=根号3
=[sinπ/9+2sin2π/9]/cosπ/9
=[sinπ/9+sin2π/9+sin2π/9]/cosπ/9
={2sin[（π/9+2π/9)/2]cos[(π/9-2π/9)/2+sin2π/9}/cosπ/9
=[cosπ/18+sin2π/9]/cosπ/9
=[sin(π/2-π/18)+sin2π/9]/cosπ/9
=2sin[(4π/9+2π/9)/2]cos[(4π/9-2π/9)/2]/cosπ/9
=[2sinπ/3cosπ/9]/cosπ/9
=根号3
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