Question

已知函数y=(tanx-tan^3 x)/(1+2tan^2 x+tan^4 x)的最大值与最小值的积为

快点高人指教啊。。在线等。。

Answer 1

呵呵，有点简单呢~
(tanx - tan³x)/(1 + 2tan²x + tan^4(x))
= (tanx - tan³x)/(1 + tan²x)²
= (tanx - tan³x)/(sec²x)²
= (tanx - tan³x) * cos^4(x)
= sinx cos³x - sin³x cosx
= sinx cosx (cos²x - sin²x)
= sinx cosx cos2x
= (1/2) sin2x cos2x
= (1/4) sin4x
最大值是1/4，最小值是-1/4
它们的积是-1/16

Answer 2

(tanx - tan³x)/(1 + 2tan²x + tan^4(x))
= (tanx - tan³x)/(1 + tan²x)²
= (tanx - tan³x)/(sec²x)²
= (tanx - tan³x) * cos^4(x)
= sinx cos³x - sin³x cosx
= sinx cosx (cos²x - sin²x)
= sinx cosx cos2x
= (1/2) sin2x cos2x
= (1/4) sin4x
最大值是1/4，最小值是-1/4
它们的积是-1/16

Answer 3

分子分母同时除以
tan^2 x
再运算