Question

How do you simplify the expression `(1-tan^2x)/(1+tan^3x)`?

Answer 1

`(1 - tan x)/(1 - tan x + tan^2 x)`

Explanation:

Use algebraic identity:
`a^3 + b^3 = (a + b)(a^2 - ab + b^2)`
In this case:
`1 + tan^3 x = (1 + tan x)(1 - tan x + tan^2 x)`
The expression can be simplified to:
`F(x) = ((1 - tan x)(1 + tan x))/((1 + tan x)(1 - tan x+ tan^2 x)) =`
`F(x) = (1 - tan x)/(1 - tan x + tan^2 x)`