(二倍角的三角函数)cosπ/5cos2/5π的值是______cosπ/5cos2π/5 =sinπ/5cosπ/5cos2π/5/sinπ/5 =4sinπ/5cosπ/5cos2π/5/4sinπ/5 =2sin2π/5cos2π/5/4sinπ/5 =sin4π/5/4sinπ/5 =sin(π-π/5)/4sinπ/5 =(1/4)sinπ/5/sinπ/5 =1/4但从4sinπ
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![(二倍角的三角函数)cosπ/5cos2/5π的值是______cosπ/5cos2π/5 =sinπ/5cosπ/5cos2π/5/sinπ/5 =4sinπ/5cosπ/5cos2π/5/4sinπ/5 =2sin2π/5cos2π/5/4sinπ/5 =sin4π/5/4sinπ/5 =sin(π-π/5)/4sinπ/5 =(1/4)sinπ/5/sinπ/5 =1/4但从4sinπ](/uploads/image/z/3885646-22-6.jpg?t=%EF%BC%88%E4%BA%8C%E5%80%8D%E8%A7%92%E7%9A%84%E4%B8%89%E8%A7%92%E5%87%BD%E6%95%B0%EF%BC%89cos%CF%80%2F5cos2%2F5%CF%80%E7%9A%84%E5%80%BC%E6%98%AF______cos%CF%80%2F5cos2%CF%80%2F5+%3Dsin%CF%80%2F5cos%CF%80%2F5cos2%CF%80%2F5%2Fsin%CF%80%2F5+%3D4sin%CF%80%2F5cos%CF%80%2F5cos2%CF%80%2F5%2F4sin%CF%80%2F5+%3D2sin2%CF%80%2F5cos2%CF%80%2F5%2F4sin%CF%80%2F5+%3Dsin4%CF%80%2F5%2F4sin%CF%80%2F5+%3Dsin%28%CF%80-%CF%80%2F5%29%2F4sin%CF%80%2F5+%3D%281%2F4%29sin%CF%80%2F5%2Fsin%CF%80%2F5+%3D1%2F4%E4%BD%86%E4%BB%8E4sin%CF%80)
(二倍角的三角函数)cosπ/5cos2/5π的值是______cosπ/5cos2π/5 =sinπ/5cosπ/5cos2π/5/sinπ/5 =4sinπ/5cosπ/5cos2π/5/4sinπ/5 =2sin2π/5cos2π/5/4sinπ/5 =sin4π/5/4sinπ/5 =sin(π-π/5)/4sinπ/5 =(1/4)sinπ/5/sinπ/5 =1/4但从4sinπ
(二倍角的三角函数)
cosπ/5cos2/5π的值是______
cosπ/5cos2π/5
=sinπ/5cosπ/5cos2π/5/sinπ/5
=4sinπ/5cosπ/5cos2π/5/4sinπ/5
=2sin2π/5cos2π/5/4sinπ/5
=sin4π/5/4sinπ/5
=sin(π-π/5)/4sinπ/5
=(1/4)sinπ/5/sinπ/5
=1/4
但从4sinπ/5cosπ/5cos2π/5/4sinπ/5
=2sin2π/5cos2π/5/4sinπ/5
=sin4π/5/4sinπ/5
=sin(π-π/5)/4sinπ/5
=(1/4)sinπ/5/sinπ/5
=1/4开始没看懂!不知道是怎么将式子变形的!
(二倍角的三角函数)cosπ/5cos2/5π的值是______cosπ/5cos2π/5 =sinπ/5cosπ/5cos2π/5/sinπ/5 =4sinπ/5cosπ/5cos2π/5/4sinπ/5 =2sin2π/5cos2π/5/4sinπ/5 =sin4π/5/4sinπ/5 =sin(π-π/5)/4sinπ/5 =(1/4)sinπ/5/sinπ/5 =1/4但从4sinπ
由公式:sin(a+b)=sina*cosb+sinb*cosa可得:sin(π/5 + π/5) = 2sin(π/5)*cos(π/5).
4sin(π/5)*cos(π/5) = 2sin(2π/5);
2sin(2π/5)*cos(2π/5)=sin(4π/5);
4sin(π/5)*cos(π/5)*cos(2π/5)/(4sinπ/5)=2sin(2π/5) *cos(2π/5)/(4sinπ/5)
=sin(4π/5)/(4sinπ/5)
而有公式:sina=sin(π-a)
sin(4π/5)/(4sinπ/5)
=sin(π/5)/(4sinπ/5)
=1/4