Question

How do you simplify `secxtan^2x+secx`?

Answer 1

`sec x tan^2 x + sec x = sec^3 x`

Explanation:

For this problem, we can use the identity

`sec^2 x - 1 = tan^2 x`

Rewriting our expression yields

`sec x tan^2 x + sec x = sec x(sec^2 x - 1) + sec x`

`= sec^3 x cancel(- sec x + sec x)`

`= sec^3 x`

We can check our answer by graphing both of them, for example.

Graph of `sec x tan^2 x + sec x`
graph{sec x * tan x * tan x + sec x [-28.87, 28.86, -14.43, 14.44]}
Graph of `sec^3 x`
graph{sec x * sec x * sec x [-28.87, 28.86, -14.43, 14.44]}