1.已知α、β为锐角,向量a=(cosα,sinα),向量b=(cosβ,sinβ),向量c=(1/2,-1/2),若向量a=向量b+向量c,求sin2α
根据：a = b + c,即(cosα,sinα) = (cosβ,sinβ) + (1/2,-1/2)
cosα = cosβ + 1/2 ① ===> cosβ = cosα - 1/2
sinα = sinβ - 1/2 ② ===> sinβ = sinα + 1/2
(cosα - 1/2 )² + (sinα + 1/2)² = 1 ===> cosα - sinα = 1/2 ③
上面③两边平方===> 1 - 2sinαcosα = 1/4
===> sin2α = 2sinαcosα = 3/4
2.向量a=(cosα,sinα),向量b=(cosβ,sinβ),|【a】-【b】|=2√5/5
若0