若直线x=t与函数y=sin(2x+π/4)和y=cos(2x+π/4)的图像分别交与P Q两点,则绝对值PQ的最大值为A 2 B 1C √3D √2

若直线x=t与函数y=sin(2x+π/4)和y=cos(2x+π/4)的图像分别交与P Q两点,则绝对值PQ的最大值为A 2 B 1C √3D √2
若直线x=t与函数y=sin(2x+π/4)和y=cos(2x+π/4)的图像分别交与P Q两点,则绝对值PQ的最大值为
A 2
B 1
C √3
D √2

若直线x=t与函数y=sin(2x+π/4)和y=cos(2x+π/4)的图像分别交与P Q两点,则绝对值PQ的最大值为A 2 B 1C √3D √2
实际上Pq的距离为两函数值之差的绝对值
当x=t时
|sin(2t+π/4)-cos(2t+π/4)|=√2|sin(2t+π/4-π/4)|=√2|sin2t|
当2t=kπ
即t=kπ/2时
|sin(2t+π/4)-cos(2t+π/4)|=√2最大

sin(2x+π/4)-cos(2x+π/4)=√2 sin2x
选D