求(sin8°+sin7°cos15°)/(cos8°-sin7°sin15°)的值
来源:学生作业帮 编辑:作业帮 分类:数学作业 时间:2024/05/08 06:07:54
求(sin8°+sin7°cos15°)/(cos8°-sin7°sin15°)的值
sin8°+sin7°cos15°
=sin(15°-7°) +sin7°cos15°
=sin15°cos7°-sin7°cos15°+sin7°cos15°
=sin15°cos7°
cos8°-sin7°sin15°
=cos(15°-7°) -sin7°sin15°
=cos15°cos7°+sin7°sin15°-sin7°sin15°
=cos15°cos7°
故
(sin8°+sin7°cos15°)/(cos8°-sin7°sin15°)
=sin15°cos7°/cos15°cos7°
=tan15°
=sin(15°-7°) +sin7°cos15°
=sin15°cos7°-sin7°cos15°+sin7°cos15°
=sin15°cos7°
cos8°-sin7°sin15°
=cos(15°-7°) -sin7°sin15°
=cos15°cos7°+sin7°sin15°-sin7°sin15°
=cos15°cos7°
故
(sin8°+sin7°cos15°)/(cos8°-sin7°sin15°)
=sin15°cos7°/cos15°cos7°
=tan15°
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