anonymous
  • anonymous
Use an angle sum identity verify the identity. cos 2 theta = 2 cos^2 theta - 1
Mathematics
  • Stacey Warren - Expert brainly.com
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katieb
  • katieb
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anonymous
  • anonymous
You should have learned by now that \(\cos2x=\cos^2x-\sin^2x\). Replace the left side, and see what you can do with it.
anonymous
  • anonymous
Im just now learning this trig stuff...didnt have to do this in high school
anonymous
  • anonymous
Have you learned that \(\cos 2x=\cos^2x-\sin^2x\) ? You wouldn't have been given a problem involving it if you haven't.

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anonymous
  • anonymous
gave us the problem in the mist of teaching that can u explain it better to me cause the teacher got mad when I kept askin them to go over it..
anonymous
  • anonymous
The thing about trig identities is that you just have to remember them. For this particular problem, you have to utilize these two: \[\begin{align*}\cos2x&=\cos^2x-\sin^2x&&\text{double angle identity for cosine}\\ \sin^2x+\cos^2x&=1&&\text{Pythagorean identity}\end{align*}\] So you're given \[\cos2\theta=2\cos^2\theta-1\] The usual procedure for proving identities is to only manipulate one side of the equation until you get something that looks exactly like the other side. First, take the double identity above; the left side immediately can be written as \[\cos^2\theta-\sin^2\theta=2\cos^2\theta-1\] Next, from the second identity, you also have that \(\sin^2\theta=1-\cos^2\theta\), so in your equation you have \[\cos^2\theta-\left(1-\cos^2\theta\right)=2\cos^2\theta-1\] Think you can take it from here?
anonymous
  • anonymous
I dont think I will ever understand trig...this kind of math is so not easy to me...
anonymous
  • anonymous
Im about to give up on this. Looking at all this cos and sin and theta is just confusing me more.
DebbieG
  • DebbieG
@SithsAndGiggles nearly did the whole thing... it's just about taking a couple of basic identities and substituting them into the expression. All you have to do is simplify on the left hand side and you should have it. :) If the \(\Large \cos\theta\)'s and the \(\Large \cos^2\theta\)'s are throwing you for a loop, just let \(\Large u=\cos\theta\) and replace them all with \(\Large u\) and \(\Large u^2\).
anonymous
  • anonymous
I get annoyed with myself when I dont pick up things as quick as I should
DebbieG
  • DebbieG
Proving trig ID's takes practice, but it's one of my favorite parts of trig! Just remember that you are showing the ALGEBRAIC STEPS that get you FROM one expression TO the other. And you can use any algebraic properties, along with any identities that you ALREADY have, to accomplish this. :) It's no different, really, than if I said: Prove that 3(x+1)-4(2-3)+4x=7x+11 You would start on the left, apply some algebra, showing each step until you have the expression on the right. Same idea! You just throw in some trig functions and some trig identities in the mix. :)
anonymous
  • anonymous
I would much rather deal with those numbers and x than all these trig identities

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