f(x)=sin(x+π/4)+cos(x+π/4)求函数奇偶性

f(x)=sin(x+π/4)+cos(x+π/4)求函数奇偶性
f(x)=sin(x+π/4)+cos(x+π/4)求函数奇偶性

f(x)=sin(x+π/4)+cos(x+π/4)求函数奇偶性
解,先化解,f(x) = sin( x + π/4 ) + cos ( x + π/4 ) = Sqrt[2] * { Sqrt[2]/2 * Sin( x + π/4 ) + Sqrt[2] * Cos[ x + π/4] } = Sqrt[2] * { Sin( x + π/4 ) * cos[ π/4 ] + Cos[ x + π/4] * sin[ π/4 ] = Sqrt[2] *sin (x + π/2)= Sqrt[2] * cos( x ) (Sqrt[2]是根号2的意思).
既有f(x) = Sqrt[2] * cos( x )
代入 f（x）=f (-x) 两边相等,为偶函数.
代入 f（-x）= -f(x) 两边不等,不是奇函数.
综上所述 为偶函数.
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