保山市2023~2024学年普通高中高三上学期B、C 类学校第三次质量监测数学.考卷答案

保山市2023~2024学年普通高中高三上学期B、C 类学校第三次质量监测数学.考卷答案试卷答案,我们目前收集并整理关于保山市2023~2024学年普通高中高三上学期B、C 类学校第三次质量监测数学.考卷答案得系列试题及其答案,更多试题答案请关注微信公众号:考不凡/直接访问www.kaobufan.com(考不凡)

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保山市2023~2024学年普通高中高三上学期B、C 类学校第三次质量监测数学.考卷答案试卷答案

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选项中有两项为多余选项

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分析利用角的等价变换,结合三角函数的公式分别化简求值.

解答解:原式=$\frac{cos(80°-15°)-sin80°sin15°}{cos(80°-75°)-sin80°sin75°}$=$\frac{cos80°cos15°}{cos80°cos75°}$=$\frac{sin75°}{cos75°}$=tan75°=tan(30°+45°)=$\frac{\frac{\sqrt{3}}{3}+1}{1-\frac{\sqrt{3}}{3}}$=2+$\sqrt{3}$;
故答案为:2+$\sqrt{3}$.

点评本题考查了三角函数式的化简求值;等积式发现角度之间的关系,进行等价变形,利用三角函数公式化简.