若f(x)=asin(x+π/4)+bcos(x-π/4) (ab不等于0是偶函数,则有序数对(a,b)可以是————(其中一对

问题描述:

若f(x)=asin(x+π/4)+bcos(x-π/4) (ab不等于0是偶函数,则有序数对(a,b)可以是————(其中一对

f(x)=asin(x+π/4)+bcos(x-π/4) =asin(x+π/4)+bsin(π/2+x-π/4) =asin(x+π/4)+bsin(x+π/4)=(a+b)sin(x+π/4),由于sin(x+π/4)不是偶函数,要使得f(x)为偶函数,需有a+b=0,所以满足此条件的都可以,当然ab≠0.比...