题目

第一题
求sin69°－sin3°＋sin39°－sin33°的值
第二题
己知sina=12/13,sin(α+β)=4/5,α与β均为锐角,求cosβ/2.

提问时间：2021-03-19

答案

1.sin69-sin3+sin39-sin33
=(sin69+sin39)-(sin33°+sin3°)
=2sin54cos15-2sin18cos15(和化积)
=2cos15(sin54-sin18)
=4cos15cos36sin18(差化积)
=(4cos15cos36sin18*cos18)/cos18
=(2cos15cos36*sin36)/cos18
=(cos15*sin72)/cos18
=(cos15*cos18)/cos18
=cos15
=sin75
=(√6+√2)/4
2.sinb
=sin[(a+b)-a]
=sin(a+b)cosa-sinacos(a+b)
由sina=12/13>sin(a+b)=4/5
且a与b均为锐角
则cos(a+b)<0,cosa>0
则sinb
=sin(a+b)cosa-sinacos(a+b)
=4/5*5/13+12/13*3/5
=56/65
则cosb=33/65
cos(b/2)>0
则cosb/2=√[(1+cosb)/2]
=(7*√65)/65