Question

求cos55°•cos65°+cos65°•cos175°+cos55°•cos175°的值．

Answer 1

cos55°•cos65°+cos65°•cos175°+cos55°•cos175°
=

1

2

（cos120°+cos10°）+cos175°（cos65°+cos55°）
=-

1

4

+

1

2

cos10°+2cos175°•cos60°•cos5°
=-

1

4

+

1

2

cos10°+cos175°cos5°
=-

1

4

+

1

2

cos10°+

1

2

（cos180°+cos170°）
=-

1

4

+

1

2

cos10°-

1

2

+

1

2

cos170°
=-

3

4

．
原式的值为-

3

4

．