Question

How do you multiply and simplify `(cosx+secx)^2`?

Answer 1

`cos^2x+2+sec^2x`

Explanation:

Expanding the binomial:

`(cosx+secx)^2=(cosx+secx)(cosx+secx)`

`=cos^2x+cosxsecx+cosxsecx+sec^2x`

Recall that `secx=1/cosx` so `cosxsecx=cosx(1/cosx)=1`:

`=cos^2x+2+sec^2x`