已知cos(x-pai/6)+sinx=4乘根号3/5,则sin(x+7pai)=

题目

已知cos(x-pai/6)+sinx=4乘根号3/5,则sin(x+7pai)=

答案

cos(x-π/6)+sinx=4√3/5
cosxcosπ/6+sinxsinπ/6+sinx=4√3/5
(√3/2)cosx+(3/2)sinx=4√3/5
(1/2)cosx+(√3/2)sinx=4/5
sin(π/6+x)=4/5
sin(7π/6+x)=-4/5