f(x)=asin(x+π/4)+3sin(x-π/4)是偶函数,求a.

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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)是偶函数,求a.f(x)=asin(x+π/4)+3sin(x-π/4)

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)是偶函数,求a.

f(x)=asin(x+π/4)+3sin(x-π/4)是偶函数,求a.
将函数右边展开=a×(√2/2sinx+√2/2cosx)+3×(√2/2sinx - √2/2cosx)
=(√2/2a+3×√2/2) sinx +(√2/2a - 3×√2/2)cosx
又由于sinx 为奇函数,cosx为偶函数,
所以sinx得系数√2/2a+3×√2/2 =0 ,解得a= - 3