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

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

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

若f(x)=asin(x+π/4)+3sin(x-π/4)是偶函数,则实数a=
f(-π/4)=asin0+3sin(-π/2)=-3
f(π/4)=asinπ/2+3sin0=a
因为f(x)是偶函数,所以,f(-π/4)=f(π/4),即a=-3.

f(x)=asin(x+pi/4)+3sin(x-pi/4)
f(-x)=-asin(x-pi/4)-3sin(x+pi/4)
对于偶函数 f(x)=f(-x)
asin(x+pi/4)+3sin(x-pi/4)=-asin(x-pi/4)-3sin(x+pi/4)
(a+3)sin(x+pi/4)=-(a+3)sin(x-pi/4)
a+3=0
a=-3