若f(x)=asin(x+π/4)+3sin(x-π/4)是偶函数,求a

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若f(x)=asin(x+π/4)+3sin(x-π/4)是偶函数,求a

若f(x)=asin(x+π/4)+3sin(x-π/4)是偶函数,求a
若f(x)=asin(x+π/4)+3sin(x-π/4)是偶函数,求a

若f(x)=asin(x+π/4)+3sin(x-π/4)是偶函数,求a
f(-x)=asin(-x+π/4)+3sin(-x-π/4)
=-asin(x-π/4)-3sin(x+π/4)
f(x)=asin(x+π/4)+3sin(x-π/4)是偶函数
所以f(x)=f(-x)
所以asin(x+π/4)+3sin(x-π/4)=-asin(x-π/4)-3sin(x+π/4)
对应系数相等
明显a=-3

a=-3,把f(x)化简,再令f(x)=f(-x)恒成立即可。