Question

PLEASE HELP ASAP!!!!!

Answer 1

`sec(x)`

Explanation:

`cos(x)+cos(x)tan^2(x)`

Multiply cos(x) by 1:

`cos(x)*1+cos(x)tan^2(x)`

Factor out cos(x):

`cos(x)(tan^2(x)+1)`

Apply the pythagorean identity (
`tan^2(x)+1=sec^2(x)`):

`cos(x)sec^2(x)`

Rewrite
`sec^2(x)`:

`cos(x)((1)/(cos(x)))^2 \\cos(x)(1)/(cos^2(x))`

Cancel cos(x):

`(1)/(cos(x))`

Rewrite:

`sec(x)`