已知f(x)=sin(x+c)+根号3sin(x-c)为偶函数,求c的值
问题描述：
已知f(x)=sin(x+c)+根号3sin(x-c)为偶函数,求c的值
答
f(x)=f(-x)
sin(x+c)+a*sin(x-c)=sin(-x+c)+a*sin(-x-c)(a=根号3)
(a+1)sin(x+c)=-(a+1)sin(x-c)
sin(x+c)+sin(x-c)=0
2sinx*cosc=0
cosc=0
c=K*pi/2k为整数.