f(x)=sin(x+ α)+cos(x-α),求使f(x)为偶函数的充分必要条件
问题描述：
f(x)=sin(x+ α)+cos(x-α),求使f(x)为偶函数的充分必要条件
答
f(x)为偶函数的充分必要条件是：f(x)=f(-x)所以f(x)=sin(x+α)+cos(x-α)=f(-x)=sin(-x+α)+cos(-x-α),又sin（-x）=-sin x,cos(-x）=cosx所以sin(x+α)+cos(α-x)=sin(α-x)+cos(x+α)展开化简得 cos α=-sin α即t...