若COS(π/4-α)=√2 /4,求sin2α/sin(π/4+α)的值_数学解答

若COS(π/4-α)=√2 /4,求sin2α/sin(π/4+α)的值

人气：206 ℃　时间：2020-02-06 11:02:36

解答

cos(π/4-α)＝√2/4→(√2/2)(cosα+sinα)＝√2/4→cosα+sinα＝1/2.sin(π/4+α)＝(√2/2)(cosα+sinα)＝√2/4.(cosα+sinα)²＝1/4→sin2α＝-3/4.∴sin2α/sin(π/4+α)＝(-3/4)/(√2/4)＝-3√2/2....