若函数f(x)=Asin(x+π/4)+3sin(x-π/4)是偶函数,求f(x)的最大值

题目

若函数f(x)=Asin(x+π/4)+3sin(x-π/4)是偶函数,求f(x)的最大值

答案

楼主,sin(a-b)=sinacosb-cosasinbcos(a-b)=cosacosb+sinasinb由以上过程易知,sinφ=a,cosφ=-3,所以tanφ=-a/3另外也可以有以下做法：f(x)=asin(x+π/4)+3sin(x-π/4)=acos(x-π/4)+3sin(x-π/4)=√（a^2+9)sin(x-π...