Question

求值：cos225°+tan240°+sin（-60°）+cot（-570°）=______．

Answer 1

cos225°+tan240°+sin（-60°）+cot（-570°）
=cos（45°+180°）+tan（60°+180°）-sin60°+cot（720°-570°）
=-cos45°+tan60°-sin60°+cot150°
=-cos45°+tan60°-sin60°+cot（180°-30°）
═-cos45°+tan60°-sin60°-cot30°
=-

2

2

+

3

-

3

2

-

3

=-

2

2

-

3

2

．
故答案為：-

2

2

-

3

2

．