※ 引述《Tiderus (修煉人生)》之銘言:
: ※ 引述《BanPeeBan (踢屁屁)》之銘言:
: : 試證明
: : tan40뀭4sin40뀽-根號3
: sin40 - 2sin80 sin40 - sin80 -sin80 2cos60sin(-20) -sin80
: = ----------------- = ---------------------- = -----------------------
: cos40 cos40 cos40
: -(sin20 + sin80) -2sin50cos30
: = ------------------ = -------------- = -2cos30 = -√3
: cos40 cos40
原式
=sin(2pi/9){[1/cos(2pi/9)]-4]
=8sin(pi/9)cos(pi/9){[2cos(pi/9)cos(4pi/9)]-1}
...分母湊成cos(pi/9)cos(2pi/9)cos(4pi/9)=1/8
=4sin(2pi/9)[cos(5pi/9)-(1/2)]
=2sin(-pi/3)+2sin(7pi/9)-2sin(2pi/9)
=-sqrt3
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