sin13°+cos30°sin17°/cos13°-sin30°sin17°化简求值

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sin13°+cos30°sin17°/cos13°-sin30°sin17°化简求值

sin13°+cos30°sin17°/cos13°-sin30°sin17°化简求值
sin13°+cos30°sin17°/cos13°-sin30°sin17°化简求值

sin13°+cos30°sin17°/cos13°-sin30°sin17°化简求值
(sin13度+sin17度×cos30度)/(cos13度-sin17度×sin30度)
=(sin(30-17)度+sin17度×cos30度)/(cos(30-17)度-sin17度×sin30度)
=sin30度cos17度/cos30度cos17度
=tan30度
=√3/3

13°=30°-17°
sin13°=sin(30°-17°)=sin13cos17-cos13sin17


cos13°=cos(30°-17°)=cos13cos17+sin13sin17
则sin13°+cos30°sin17°/cos13°-sin30°sin17°
=sin13cos17/cos13cos17°
=tan13°