若f(x)=asin(x+π/4)+bcos(x-π/4)(ab不等於0是偶函數,則有序數對(a,b)可以是————(其中一對

若f(x)=asin(x+π/4)+bcos(x-π/4)(ab不等於0是偶函數,則有序數對(a,b)可以是————(其中一對

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),由於sin(x+π/4)不是偶函數,要使得f(x)為偶函數,需有a+b=0,所以滿足此條件的都可以,當然ab≠0.比…