Question

sec^2(x)+sec(x)-2

Answer 1

Factor the algebraic expression below in terms of a single trigonometric function. Sorry for prior lack of information

Answer 2

It's just like x^2 + x - 2

Answer 3

Factor x^2 + x - 2

Answer 4

well?

Answer 5

But that would make it (sec(x)+1)(sec(x)-) correct?

Answer 6

No. Can you factor x^2 + x - 2?

Answer 7

Isn't it (x + 2)(x - 1)?

Answer 8

And there has to be only one trig function. I meant (x-2)

Answer 9

I know...but when you factor sec^2x + sec x -2 it resembles x^2 + x - 2,

just that instead of sec x , we have just x

So the factors of sec^2x + sec x - 2

will be (sec x + 2)(sec x - 1)

Answer 10

The question means that, in theory, there shouldn't be a second sec, correct?

Answer 11

I now understand I made a silly mistake in factoring

Answer 12

Welcome.

Answer 13

But still there's the getting rid of the second sec. How does that work?

Answer 14

Let's multiply using FOIL" (sec x + 2)(sec x - 1)


you get: sec^2x - sec x + 2 sec x - 2
= sec^2 x + sec x - 2

Answer 15

Correct, however the question states it requires using a single trig function. There are still two in the equation, correct? How do I change this?

Answer 16

Or am I misunderstanding what is being asked?

Answer 17

\[(\sec x+2)(\sec x-1)=0\]\[\sec x+2=0 \]
or\[\sec x-1=0\]
\[\sec x=-2\]
or
\[\sec x=1\]

Answer 18

I believe you just wanted the factors.

Answer 19

Thank you all!

Answer 20

If sec x = -2, cos x = - 1/2 and x = 120 deg or 240 deg
If sec x = 1, cos x = 1 and x = 0 degrees