Question

FACTOR the algebraic expression below in terms of a single trigonometric function.

Answer 1

\[\cos x - \sin^2x - 1\]

Answer 2

\[\sin ^{2} x = \cos ^{2}x - \cos 2x\] Use that relationship to substitute for the sin and you will have an equation that has only the cos

Answer 3

So with that I can make the equation \[\cos x - \cos^2x - \cos2x\]

Answer 4

Thanks for replying by the way

Answer 5

Actually, there is a better way than my first post, now that I think about it.

Answer 6

sin^2 x + cos^2 x = 1. Or, rewritten: sin^2 x = 1 - cos^2 x. Make that substitution instead and then it can be factored, which is your goal anyway.

Answer 7

So then I get \[cosx−1 - \cos^2x−1\] ?

Answer 8

and then I factor that?

Answer 9

Careful with your + and - signs, you're a little bit off, but very close. After you correct that and combine the two -1's, you can factor the cos x.

Answer 10

\[cosx+\cos^2x−2\] ?

Answer 11

yes, and then for the first 2 terms, cos x + cos^2 x = (cos x)(1 + cos x)

Answer 12

So the whole thing becomes (cos x)(1 + cos x)-2?

Answer 13

yes.

Answer 14

And that is the final answer?

Answer 15

yes.

Answer 16

Thank you so much for your help. I can't thank you enough.

Answer 17

you're welcome!