Question

不查表求值：cos40°•cos80°+cos80°•cos160°+cos160°•cos40°．

Answer 1

原式=

1

2

[cos120°+cos（-40°）+cos240°+cos（-80°）+cos200°+cos120°]
=

1

2

（-cos60°+cos40°-cos60°+cos80°-cos20°-cos60°）
=

1

2

[-

3

2

+cos（60°-20°）+cos（60°+20°）-cos20°]
=

1

2

[-

3

2

+cos60°cos20°+sin60°sin20°+cos60°cos20°-sin60°sin20°-cos20°]
=

1

2

[-

3

2

+cos20°-cos20°]
=-

3

4