Question

若函数f(x)＝sin(x＋α)－2cos(x－α)是奇函数，则sin α·cos α＝________．

Answer 1

∵f(x)是奇函数，∴f(0)＝0，则sin α＝2cos α，tan α＝2，由1＋tan²α＝，得cos²α＝，∴sin α·cos α＝2cos²α＝．