Question

f(x)=sin(x+ α)+cos(x-α),求使f(x)为偶函数的充分必要条件

Answer 1

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tan α=-1