Question

已知f(x)=sin(x+c)+根号3sin(x-c)为偶函数,求c的值

Answer 1

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/2 k为整数.