已知COS(X-π/6)+SINX=4乘以根3除以5,则SIN(X+7π6)的值=?

题目

已知COS(X-π/6)+SINX=4乘以根3除以5,则SIN(X+7π6)的值=?

答案

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