已知sin(a+3TT4)=5/13,cos(TT/4-β)=3/5,且-TT/4扫码下载作业帮搜索答疑一搜即得
问题描述：
已知sin(a+3TT4)=5/13,cos(TT/4-β)=3/5,且-TT/4 扫码下载作业帮
搜索答疑一搜即得
答
sin(a+3TT4)=5/13?应该是sin(a+3π/4)=5/13 吧!
已知-π/4π/2这就是说角a+ 3π/4是第二象限角,角π/4-β是第四象限角
故有：cos(a+ 3π/4)已知sin(a+ 3π/4)=5/13,cos(π/4-β)=3/5,那么：
cos(a+ 3π/4)=-根号[1-sin²(a+ 3π/4)]=-12/13,
sin(π/4-β)=-根号[1-cos²(π/4-β)]=-4/5
所以：-sin(a-β)
=sin(π+a-β)
=sin[(a+ 3π/4)+(π/4-β)]
=sin(a+ 3π/4)*cos(π/4-β)+ cos(a+ 3π/4)*sin(π/4-β)
=(5/13)*(3/5) + (-12/13)*(-4/5)
=63/65
即sin(a-β)=-63/65
那么：cos2(a-β)=1-2sin²(a-β)=1-2×(-63/65)²=-3713/4225