已知cos(a-π/6)+sina=(4*根号3)/5,则sin(a+7π/6)的值是( ) A -(2根号3)/5 B (2根号3)/5 C -4/5 D 4/5

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已知cos(a-π/6)+sina=(4*根号3)/5,则sin(a+7π/6)的值是( ) A -(2根号3)/5 B (2根号3)/5 C -4/5 D 4/5

已知cos(a-π/6)+sina=(4*根号3)/5,则sin(a+7π/6)的值是( ) A -(2根号3)/5 B (2根号3)/5 C -4/5 D 4/5
已知cos(a-π/6)+sina=(4*根号3)/5,则sin(a+7π/6)的值是( )
A -(2根号3)/5
B (2根号3)/5
C -4/5
D 4/5

已知cos(a-π/6)+sina=(4*根号3)/5,则sin(a+7π/6)的值是( ) A -(2根号3)/5 B (2根号3)/5 C -4/5 D 4/5
根据:cos(a-π/6)+sina=(4*根号3)/5
有:cosacosπ/6+sinasinπ/6+sina=(4*根号3)/5
(根号3)/2cosa+3/2sina=(4*根号3)/5
得到:cosa+(根号3)sina=8/5
所以:
sin(a+7π/6)=sinacos7π/6+cosasin7π/6=(-根号3)/2sina-1/2cosa
=(-1/2)(cosa+根号3sina)
=(-1/2)*8/5
=-4/5

B