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来源：学生作业帮 编辑：拍题作业网作业帮 分类：数学作业 时间：2024/06/11 01:26:42
求证：tan37.5=根号6+根号3-根号2-2
解题思路： 很麻烦的。一步一步推。。。直到推出所要的根号6，根号3，根号2和2
解题过程：
tan37.5°
=tan75°/2
=(1-cos75°)/sin75°
=[1-cos(45°+30°)]/sin(45°+30°)
=(1-cos45°cos30°+sin45°sin30°)/(sin45°cos30°+cos45°sin30°)
=(1-√2/2*√3/2+√2/2*1/2)/(√2/2*√3/2+√2/2*1/2)
=(1-√6/4+√2/4)/(√6/4+√2/4)
=[(4+√2-√6)/4]/[(√6+√2)/4]
=(4+√2-√6)/(√6+√2)
=(4√6+2√3-6-4√2-2+2√3)/4
=(4√6+4√3-4√2-8)/4
=√6+√3-√2-2
最终答案：略
解题过程：
tan37.5°
=tan75°/2
=(1-cos75°)/sin75°
=[1-cos(45°+30°)]/sin(45°+30°)
=(1-cos45°cos30°+sin45°sin30°)/(sin45°cos30°+cos45°sin30°)
=(1-√2/2*√3/2+√2/2*1/2)/(√2/2*√3/2+√2/2*1/2)
=(1-√6/4+√2/4)/(√6/4+√2/4)
=[(4+√2-√6)/4]/[(√6+√2)/4]
=(4+√2-√6)/(√6+√2)
=(4√6+2√3-6-4√2-2+2√3)/4
=(4√6+4√3-4√2-8)/4
=√6+√3-√2-2
最终答案：略