帮尽快求一下三角运算的值求值：cos(pi/11)cos(2pi/11)cos(3pi/11)cos(4pi/11)cos(5pi/11)一共是5个余弦相乘,pi=3.141592653……5个运算角度成等差数列.求最后的值.

Question

帮尽快 求一下三角运算的值
求值：
cos(pi/11)cos(2pi/11)cos(3pi/11)cos(4pi/11)cos(5pi/11)
一共是5个余弦相乘,pi= 3.141592653…… 5个运算角度成等差数列.
求最后的值.

Answer 1

设原式=A
则
sin(pi/11)*A=
[sin(pi/11)cos(pi/11)]cos(2pi/11)cos(3pi/11)cos(4pi/11)cos(5pi/11)
=1/2*sin(2pi/11)cos(2pi/11)cos(3pi/11)cos(4pi/11)cos(5pi/11)
=1/4*sin(4pi/11)cos(4pi/11)cos(3pi/11)cos(5pi/11)
=1/8*sin(8pi/11)cos(3pi/11)cos(5pi/11)
{运用sin(8pi/11)=sin(3pi/11)}
=1/16*sin(6pi/11)cos(5pi/11)
{运用sin(6pi/11)=sin(5pi/11)}
=1/32*sin(10pi/11);
=1/32*sin(pi/11);
所以sin(pi/11)A=1/32*sin(pi/11);
所以A=1/32