α∈(0,π),且2sin(π/3-α)+sinα=3/2,求α

题目

α∈(0,π),且2sin(π/3-α)+sinα=3/2,求α

答案

2sin(π/3-α)+sinα=3/2
sin(π/3-α)+1/2 sin(α) = 3/4
sin(π/3)cos(a) - 1/2sin(a)+1/2sin(a) = 3/4; 展开
sin(π/3)cos(a) = 3/4;
接下来不用我说了