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

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

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

若函数f(x)=Asin(x+π/4)+3sin(x-π/4)是偶函数,求f(x)的最大值
楼主,
sin(a-b)=sinacosb-cosasinb
cos(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/4+φ),其中tanφ=a/3
∵f(x)是偶函数 ∴φ-π/4=Kπ+π/2 (K∈Z)
∴φ=Kπ+3π/4,∴tanφ=tan3π/4=-1
∴a=-3