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

题目详情
求值:cos225°+tan240°+sin(-60°)+cot(-570°)=______.
▼优质解答
答案和解析
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

故答案为:-
2
2
-
3
2