Basic Trig problem

**M670** · November 11th 2012, 06:19 PM

Simplify and write the trigonometric expression in terms of sine and cosine:

I put this as my answer

and I was told this Your answer isn't a number
(it looks like a formula that returns a number) I am figuring I have to reduce this?

**richard1234** · November 11th 2012, 06:54 PM

The answer is actually -1. To show this, we have

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

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

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

$= -1$

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