# Basic Trig problem

• Nov 11th 2012, 06:19 PM
M670
Basic Trig problem
Simplify and write the trigonometric expression in terms of sine and cosine:
http://webwork.mathstat.concordia.ca...ac79325181.png

I put this as my answer
(it looks like a formula that returns a number) I am figuring I have to reduce this?
• Nov 11th 2012, 06:54 PM
richard1234
Re: Basic Trig problem
The answer is actually -1. To show this, we have

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

$= \frac{\sin^2 x - 1}{\cos^2 x}$

$= \frac{-\cos^2 x}{\cos^2 x}$

$= -1$