若函数f(x)=sin(x+α)-2cos(x-α)是偶函数,则cos2α=_______________.若函数 f(x) =sin( x + α ) - 2cos( x - α )是偶函数,则cos 2α =_______________.越详细越好...希望有人回答.
问题描述：
若函数f(x)=sin(x+α)-2cos(x-α)是偶函数,则cos2α=_______________.
若函数 f(x) =sin( x + α ) - 2cos( x - α )是偶函数,则cos 2α =_______________.
越详细越好...希望有人回答.
答
函数f(x)=sin(x+α)-2cos(x-α)是偶函数f(-α)=f(α)sin(-α+α)-2cos(-α-α)=sin(α+α)-2cos(α-α)0-2cos2α=sin2α-2sin2α=2-2cos2α(sin2α)²+(cos2α)²=1(2-2cos2α)²+(cos2α)²=15cos&...