Question

PLEASE HELP ASAP!!!!!

Answer 1

Answer:

$sec(x)$

Step-by-step 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 $sec^2(x)$:

$cos(x)(\frac{1}{cos(x)})^2 \\cos(x)\frac{1}{cos^2(x)}$

Cancel cos(x):

$\frac{1}{cos(x)}$

Rewrite:

$sec(x)$