Math Help - Quick Trig Question, help please

1. Quick Trig Question, help please

What would be in the box? I'm looking for an answer in terms of things like csc, sec, tan, etc. i think it's sec^2 but i'm not sure. thanks!

2. Originally Posted by gobbajeezalus

What would be in the box? I'm looking for an answer in terms of things like csc, sec, tan, etc. i think it's sec^2 but i'm not sure. thanks!
Hi gobbajeezalus,

It is indeed sec^2.

Since
$\tan^2(x)$
$=\frac{sin^2(x)}{cos^2(x)}$
$=\frac{1-cos^2(x)}{cos^2(x)}$
$=\frac{1}{cos^2(x)}-\frac{cos^2(x)}{cos^2(x)}$
$=sec^2(x)-1$