Solving Trig Problem: Tan^2(x) - Sec^2(x)

[migia]

Homework Statement

The original problem wants me to simplify tan^2(x)-sec^2(x). I have simplified it down to
(sin^2(x)-1)/(cos^2(x)). The answer says its solution is -1. My problem is I cannot understand how to get -1 out of (sin^2(x)-1)/(cos^2(x)). Thank you in advance.

Homework Equations

The Attempt at a Solution

I have tried manipulating the Pythagorean identities, I am still confused.

 

[SteamKing]

Don't you know a relationship between sin^2, cos^2 and 1?

 

[migia]

yes, it should be sin^2(x)+cos^2(x)=1

 

[armolinasf]

try factoring a negative one from the numerator

 

[migia]

oh i just figured it out.
the identity tan^2(x)+1=sec^2(x) all I had to do was move 1 to right and sec^2(x) to the left!
Thank you guys for the help too.

 

[armolinasf]

There are several ways to do this one actually you could have substituted sec^2x-1 for tan^2x, or you could have taken (sin^2(x)-1)/(cos^2(x)) and factored -1 from the numerator giving you -1(1-sin^2x)/cos^2x =>-1(cos^2x/cos^2x)=-1/1=-1. So just remember that there are always a ton of different ways to approach these identity problems.

 

[migia]

Ok, thank you for your help. I do really appreciate it.

 

[SteamKing]

If you have (sin^2 - 1)/cos^2, then you can rewrite and expand as (sin^2 - (sin^2 + cos^2))/cos^2 = (sin^2 - sin^2 - cos^2)/cos^2 = -cos^2 / cos^2 = -1, so long as cos^2(x) is not equal to zero.