= (sin10)^2 + (sin50)^2 + sin10sin50
= (sin10)^2 + (sin50)^2 - 2sin10sin50cos120
想像一个三角形,三个角分别是10,50,120,
对应的三边长sin10,sin50,sin120
由余弦定理得
(sin120)^2 = (sin10)^2 + (sin50)^2 - 2sin10sin50cos120
所以原式就等于 (sin120)^2 = 3/4（sin10sin50）怎么变成（sin10*sin50 = -2*sin10*sin50*(-1/2) = -2*sin10*sin50*cos120