三角函数最值问题已知x,y,z为实数,求：f(x,y,z)=[sin(x-y)]^2+[sin(y-z)]^2+[sin(z-x)_数学解答

三角函数最值问题
已知x,y,z为实数,求：f(x,y,z)=[sin(x-y)]^2+[sin(y-z)]^2+[sin(z-x)]^2的最大值.

人气：441 ℃　时间：2020-04-10 13:28:10

解答

sin^2(x-y)+sin^2(y-z)+sin^2(z-x)=[1-cos2(x-y)+1-cos2(y-z)+1-cos2(z-x)]/2=3/2-[(cos2xcos2y+sin2xsin2y)+(cos2ycos2z+sin2ysin2z)+(cos2zcos2x+sin2zsin2x)]/2=3/2-[(2cos2xcos2y+2cos2ycos2z+2cos2zcos2x)+(2si...