Question

y=sin^6(x)+cos^6(x)求值域

Answer 1

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