已知sinα（x+π/6）=1/4,则sin（5π/6-x）+sin（π/3-x）的平方=?
问题描述：
已知sinα（x+π/6）=1/4,则sin（5π/6-x）+sin（π/3-x）的平方=?
答
sin²（5π/6-x）+sin²（π/3-x）=-sin(x-5π/6)+cos(X+π/6)=sinπ+(x-5π/6)+cos(X+π/6)
=sinα²（x+π/6）+cos²(X+π/6)=1
答
(x+π/6)+(5π/6-x)=π,(x+π/6)+(π/3-x)=π/2
根据诱导公式：
sin(5π/6-x)=sin[π-(x+π/6)]=sin(x+π/6)=1/4
sin^2(π/3-x)=sin^2[π/2-(x+π/6)]=cos^2(x+π/6)=1-sin^2(x+π/6)=1-1/16=15/16
所以sin(5π/6-x)+sin^2(π/3-x)=1/4+15/16=19/16