Question

cos²80°+sin²50°-sin190°·cos320°

Answer 1

= (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