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(sin10°+cos50°)/(cos10°-sin50°)?

来源:学生作业帮 编辑:作业帮 分类:数学作业 时间:2024/07/08 11:57:19
(sin10°+cos50°)/(cos10°-sin50°)?
sin10°+cos50°
=sin10°+sin40°
=2sin25cos15
cos10°-sin50
=sin80-sin50
=2cos65sin15
=2sin25sin15
(sin10°+cos50°)/(cos10°-sin50°)
=2sin25cos15/2sin25sin15
=ctg15
=1/tan15
=1/tg(45-30)
=(1+tan45tan30)/(tan45-tan30)
=2+√3