cos20°•cos40°•cos60°•cos80°=( ) A.14 B.18 C.116 D.132
问题描述:
cos20°•cos40°•cos60°•cos80°=( )
A.
1 4
B.
1 8
C.
1 16
D.
1 32
答
∵cos20°•cos40°•cos80°=
=2sin20°cos20°cos40°cos80° 2sin20°
=2sin40°cos40°cos80°
22sin20°
2sin80°cos80°
23sin20°
∴cos20°•cos40°•cos80°=
×1 8
=sin160° sin20°
×1 8
=sin(180°−20°) sin20°
1 8
又∵cos60°=
1 2
∴cos20°•cos40°•cos60°•cos80°=
×1 2
=1 8
1 16
故选C