一道三角函数,硬靠公式推导的已知cos(α-π/6)+sinα=4√3/5,则sin(α+7π/6)=?

Question

一道三角函数,硬靠公式推导的
已知cos(α-π/6)+sinα=4√3/5,则sin(α+7π/6)=?

Answer 1

cos(α-π/6)+sinα=4√3/5
cosαcosπ/6 + sinαsinπ/6 +sinα =4√3/5
cosα√3/2 + sinα/2 + sinα =4√3/5
cosα√3/2 +3sinα/2 =4√3/5
两边除以√3得：
cosα/2 +sinα√3 /2 =4/5
cosαsin π/6 +sinαcosπ/6 =4/5
sin(α+π/6) =4/5
sin(α+7π/6) =-4/5