Question

已知f（α）= sin(180°-α)sin(270°-α)tan(180°-α) sin(90°+α)tan(180°+α)tan(360°-α)

已知f（α）= sin(180°-α)sin(270°-α)tan(180°-α) sin(90°+α)tan(180°+α)tan(360°-α) ，则f（- 31π 6 ）的值为______．

Answer 1

由题意得：f（α）= sinα(-cosα)(-tanα) cosαtanα(-tanα) =-cosα， 则f（- 31π 6 ）=-cos（- 31π 6 ）=-cos（5π+ π 6 ）=-cos（π+ π 6 ）=cos π 6 = 3 2 ． 故答案为： 3 2