Question

设函数f(x)=cos(x+φ)(0＜φ＜π),若f(x)+f′(x)是奇函数,则φ=_________.

Answer 1

思路解析:f′(x)=-sin(x+φ)(x+φ)′=-sin(x+φ),

h(x)=f(x)+f′(x)

=2［coscos(x+φ)-sinsin(x+φ)］

=2cos(x+φ+).

要使h(x)为奇函数,需且仅需φ+=kπ+(k∈Z),即φ=kπ+(k∈Z).

又0＜φ＜π,所以k只能取0,从而φ=.

答案: