y=tanx-tanx^3/(1+2tanx^2+tanx^4)的最大值与最小值的积是

y = (tanx - tan³x)/(1 + 2tan²x + tan^4x)
= (tanx - tan³x)/(1 + tan²x)²
= (tanx - tan³x)/(sec²x)²
= (tanx - tan³x) * cos^4x
= sinxcos³x - sin³xcosx
= (sinxcosx)(cos²x - sin²x)
= (1/2)(sin2x)(cos2x)
= (1/4)sin4x
最小值 = -1/4
最大值 = 1/4
最小值与最大值的积 = (-1/4)(1/4) = -1/16