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

．