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Can someone help me please? Rewrite with only sin x and cos x. cos 2x + sin x

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Okay. So this stems from trigonometric identities and double angle formulas. Do you know any double angle formulas?
Not really, no. Sorry
No prolem. A really good reference for all of these formulas would be this: (one minute.)

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*No problem. Anyways, here's the webpage with pretty much every possible identity you can imagine for Trig. You'll notice that under the double angle formulas section, Cos(2x) has three different accompanying equations. Can I ask what math you're in right now, i'm assuming Precalc?
You are correct, I'm in precalc. And thanks for the link btw. That is awesome.
\[\cos(2x) = \cos ^{2}(x) - \sin ^{2}(x)\]\[\cos(2x) = 2\cos ^{2}(x)-1\]\[\cos(2x) = 1 - 2\sin ^{2}(x)\]
No problem. Okay, given these formulas, we can substitute cos(2x) for other things without double angles. Right now, we've got \[\cos(2x) + \sin(x)\], correct?
(Sorry for asking something you obviously know the answer to, just giving myself time to think LOL. I haven't done this in a while.)
No you're doing great. You're helping me way more than anyone has thus far. Take all the time you need I really appreciate your helping me out man.
No worries. I'm a little confused about the vague instructions. While you can rewrite it with those terms, i'm wondering if it's acceptable to have only sine, only cosine, or whether cosine or sine squared is acceptable. After all, that is basically what these are. Guess every case might be worked out.
If it helps, the possible answers are: 1 + 3 sin x 1 + 3 sin2x 1 - 2 sin2x + sin x 1 + 2 sin2x + sin x
The last 3 are (sin^2 x) btw
Oh, lol, okay then. That's WAY simpler than what I was about to do. My bad, I was like, half-trying to solve a trig identity. So yeah, just take a look at the formulas I put up, and substitute them. From there it's super easy to see which one makes sense with the possible answers.
Don't try to solve anything, just see which substitution would get you closest to the answers given. It should be a single step.
You follow?
I think so. So the answer would just be 1 - 2 sin2x + sin x
Exactly, but I have to say, don't be afraid of using the carat symbol (^) if you're ever writing something on a computer and can't put in a fancy superscript like: \[\sin ^{2}x\] to denote when a value is squared. People could very, very easily misread it as sin(2x) instead of sin^2(x), and that could mess up a whole problem.
Thanks for the tip and all your help. I can't thank you enough.
No problem. Good luck with Precalc. I struggled a lot with it when I first learned it.
(Heck, i'm still learning it, albeit different forms.)
Haha. I guess it never really ends does it?
Nope. We're dumb forever. :P PS, I don't know if this would apply to you, but do you use flash cards to study?
sometimes. I guess it depends on what I am studying. If there are a lot of vocabulary words or something I will usually use flashcards.

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