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（1）COT10度+TAN15度=?A.1/SIN5度B.1/COS5度C.1/SIN10度D.1/COS10度（2）COS36度-COS72度=?（3）COS24度+COS48度-COS12度-COS84度=?
题目详情
▼优质解答
答案和解析
2sin36(COS36-COS72)
=sin72-2sin36cos72
=sin72-(sin108+sin(-36))=sin36
故cos36-cos72=1/2
(3)cos24+cos48-cos12-cos84
=(cos24-cos84)+(cos48-cos12)
=-2sin54sin(-30)-2sin30sin18(和差化积)
=sin54-sin18
=cos36-cos72
=1/2 (见上题)
=sin72-2sin36cos72
=sin72-(sin108+sin(-36))=sin36
故cos36-cos72=1/2
(3)cos24+cos48-cos12-cos84
=(cos24-cos84)+(cos48-cos12)
=-2sin54sin(-30)-2sin30sin18(和差化积)
=sin54-sin18
=cos36-cos72
=1/2 (见上题)
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