y=sin^6(x)+cos^6(x)求值域
问题描述：
y=sin^6(x)+cos^6(x)求值域
答
y=(sin^2 x+cos^2 x)^3-3sin^4 xcos^2 x-3sin^2 xcos^4 x
=1-3sin^2 xcos^2 x(sin^2 x+cos^2 x)
=1-3/4*sin^2 4x
=1-3/4*(1-cos8x)/2
=5/8+3/8*cos8x
y amx=1
y min=1/4
1/4