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

题目简介

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

题目详情

求值:cos225°+tan240°+sin(-60°)+cot(-570°)=______.
题型:填空题难度:中档来源:不详

答案

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

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