已知sin（x+π/3）=1/4,怎么求sinx的值?

题目

已知sin（x+π/3）=1/4,怎么求sinx的值?

答案

sin²(x+π/3)+cos²(x+π/3)=1
所以cos(x+π/3)=±√15/4
所以sinx
=sin[(x+π/3)-π/3]
=sin(x+π/3)cosπ/3-cos(x+π/3)sinπ/3
=(1+√45)/8或(1-√45)/8