已知sin a—cosB=1/2 ,sinB+cos a=√3/2.求sin(a—B)的值?√3为根号3!a为α B为β
来源:学生作业帮助网 编辑:作业帮 时间:2024/08/27 03:34:08
已知sin a—cosB=1/2 ,sinB+cos a=√3/2.求sin(a—B)的值?√3为根号3!a为α B为β
已知sin a—cosB=1/2 ,sinB+cos a=√3/2.求sin(a—B)的值?
√3为根号3!a为α B为β
已知sin a—cosB=1/2 ,sinB+cos a=√3/2.求sin(a—B)的值?√3为根号3!a为α B为β
(sina-cosB)^2=sin^2 a-2sinacosB+cos^2 B=1/4
(sinB+cosa)^2=sin^2 B+2sinBcosa+cos^2 a=3/4
以上两式相加,得
2-2(sinacosB-sinBcosa)=1
则 sinacosB-sinBcosa=sin(a-B)=1/2