函数y=sin2x(sin2x+cos2x)的周期是

题目

函数y=sin2x(sin2x+cos2x)的周期是
如题,要过程的啦,然后答案是 派/2 .谢谢.

答案

y=sin²2x+sin2xcos2x
=(1-cos4x)/2+1/2*sin4x
=√2/2(sin4x*√2/2-cos4x*√2/2)+1/2
=√2/2(sin4xcosπ/4-cos4xπ/4)+1/2
=√2/2*sin(4x+π/4)+1/2
所以T=2π/4=π/2