Answer:
[tex]sec(x)[/tex]
Step-by-step explanation:
[tex]cos(x)+cos(x)tan^2(x)[/tex]
Multiply cos(x) by 1:
[tex]cos(x)*1+cos(x)tan^2(x)[/tex]
Factor out cos(x):
[tex]cos(x)(tan^2(x)+1)[/tex]
Apply the pythagorean identity ([tex]tan^2(x)+1=sec^2(x)[/tex]):
[tex]cos(x)sec^2(x)[/tex]
Rewrite [tex]sec^2(x)[/tex]:
[tex]cos(x)(\frac{1}{cos(x)})^2 \\cos(x)\frac{1}{cos^2(x)}[/tex]
Cancel cos(x):
[tex]\frac{1}{cos(x)}[/tex]
Rewrite:
[tex]sec(x)[/tex]
