tan765+tan675-tan(-300)-tan660+tan(225)3次方

题目

tan765+tan675-tan(-300)-tan660+tan(225)3次方

答案

tan765°+tan675°-tan(-300°)-tan660°+tan³(225°)
=tan(765°-720°)+tan(675°-720°)-tan(-300°+360°)-tan(660°-720°)+tan³(225°-180°)
= tan45°+tan(-45°)-tan60°-tan(-60°)+tan³45°
= tan45°-tan45°-tan60°+tan60°+tan³45°
=tan³45°
=(√2/2)³
=√2/4
答案：√2/4