作业帮三角函数,第八题,谢谢,求详解,最好配图
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三角函数,第八题,谢谢,求详解,最好配图
三角函数,第八题,谢谢,求详解,最好配图
三角函数,第八题,谢谢,求详解,最好配图
tan2π/9=(sin2π/9) / (cos2π/9)
sin2π/9= 2sinπ/9 * cosπ/9
(2cosπ/9+1)*tan2π/9 -2sinπ/9
cos2x= 2cos²x -1
2cos²π/9 -cos2π/9=1
原式=2sinπ/9 * (1+cosπ/9) / (cos2π/9)
1+cosπ/9=2cos²π/18=2cosπ/18 *sin4π/9=4cosπ/18 *sin2π/9 *cos2π/9,
原式=2sinπ/9 * (1+cosπ/9) / (cos2π/9)
=8sinπ/9 *cosπ/18 *sin2π/9
积化和差2sinπ/9 *sin2π/9= cosπ/9 -cosπ/3,故
8sinπ/9 *cosπ/18 *sin2π/9
=4(cosπ/9 -cosπ/3) *cosπ/18 代入cosπ/3=1/2
= -2cosπ/18 +4cosπ/9 *cosπ/18
积化和差2cosπ/9 *cosπ/18= cosπ/6 +cosπ/18
-2cosπ/18 +4cosπ/9 *cosπ/18
= -2cosπ/18 + 2cosπ/6 + 2cosπ/18
= 2cosπ/6
= √3
