Question

How do you simplify the expression `secxtanxcosx`?

Answer 1

`sec x tan x cos x` simplifies to `tan x`.

Explanation:

Recall that `sec x = 1/(cos x)`. We will begin by rearranging the factors so that `sec x` and `cos x` are beside each other and then proceed with substituting the definition for `sec x`.

`sec x tan x cos x`
`tan x sec x cos x`
`tan x (1/(cos x)) cos x`
`tan x ((cos x)/(cos x))`
`tan x (1)`
`tan x`