余弦100度乘以余弦140度乘以余弦160度等于多少?

-0.125
关键：正弦的二倍角公式,正弦与余弦的转化
原式=(-sin10)*(-cos40)*(-cos20)
=(-sin10)*(-cos40)*(-cos20)*(cos10)/(cos10)
将sin10与cos10放在一起
= -(sin10*cos10)*cos20*cos40/cos10
=-(1/2 sin20)*cos20*cos40/cos10
=-(1/2sin20*cos20)*cos40/cos10
=-(1/4sin40)*cos40/cos10
=-(1/8sin80)/cos10
=-1/8cos10/cos10
=-1/8=-0.125
输入了那么多,楼下的不要抄袭啊,也不要变相抄袭,复制一点,省略一点

cos100*cos40*cos60=cos(180-80)*cos(180-40)*cos(180-20)=-cos80cos40cos20(诱导公式）=-cos80cos40cos20sin20sin20=-12(cos80cos40sin40)sin20=-12*12(cos80sin80)sin20=-12*12*12(sin160sin20)=-18(sin(180-20)sin20)=-18(sin20sin20)=-18=-0.125