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anonymous
 one year ago
how would i begin to prove the equation 2/1+cosx  tan^2 x/2=1
anonymous
 one year ago
how would i begin to prove the equation 2/1+cosx  tan^2 x/2=1

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xapproachesinfinity
 one year ago
Best ResponseYou've already chosen the best response.2so it is \[\frac{1}{1+\cot x}\tan^2x=1\]

xapproachesinfinity
 one year ago
Best ResponseYou've already chosen the best response.2the first thing im thinking about is multiplying by 1cotx top and bottom for the 1/1+cotx

xapproachesinfinity
 one year ago
Best ResponseYou've already chosen the best response.2i haven't started yet i was just asking is that the right thing? because the way you wrote it can be misleading

xapproachesinfinity
 one year ago
Best ResponseYou've already chosen the best response.2oh hold on i missed 2 on top

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0well it's like \[(2/1+cosx)  \tan^2 x/2=1\]

xapproachesinfinity
 one year ago
Best ResponseYou've already chosen the best response.2\[\frac{2}{1+\cot x}\frac{\tan^2x}{2}=1\]

xapproachesinfinity
 one year ago
Best ResponseYou've already chosen the best response.2may bad! cos not cot

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0right right i got it

xapproachesinfinity
 one year ago
Best ResponseYou've already chosen the best response.2i must be blind or something lol

xapproachesinfinity
 one year ago
Best ResponseYou've already chosen the best response.2\[\frac{2}{1+\cos x}\frac{\tan^2x}{2}=1\] looking at the left side \[\frac{2}{1+\cos x}\frac{\tan^2x}{2}=\frac{2(1\cos x)}{(1+\cos x)(1\cos x)}\frac{\tan^2x}{2}\]

xapproachesinfinity
 one year ago
Best ResponseYou've already chosen the best response.2let's go from there

xapproachesinfinity
 one year ago
Best ResponseYou've already chosen the best response.2\[\frac{2(1\cos x)}{1\cos^2x}\frac{\tan^2x}{2}\] \[\frac{22\cos x}{\sin^2x}\frac{\tan^2x}{2}\] \[\frac{22\cos x}{\sin^2x}\frac{\sin^2x}{2\cos^2x}\]

xapproachesinfinity
 one year ago
Best ResponseYou've already chosen the best response.2can you go further your self

xapproachesinfinity
 one year ago
Best ResponseYou've already chosen the best response.2actually that's not an identity

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0i didnt think so lol

xapproachesinfinity
 one year ago
Best ResponseYou've already chosen the best response.2oh no i take it back it is! when i plugged in 0 i forgot something lol

xapproachesinfinity
 one year ago
Best ResponseYou've already chosen the best response.2hmm for pi/4 it is not good!

xapproachesinfinity
 one year ago
Best ResponseYou've already chosen the best response.2are you sure you typed the right thing!

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0i will show you exactly what's in the textbook but how do you get the horizontal division line in the equation like you did in all your formulas?

xapproachesinfinity
 one year ago
Best ResponseYou've already chosen the best response.2use drawing tool if you have a mouse you will do find drawing the problem

xapproachesinfinity
 one year ago
Best ResponseYou've already chosen the best response.2snap shot your problem don't you have a phone?

xapproachesinfinity
 one year ago
Best ResponseYou've already chosen the best response.2what you have there is not an identity i verified it with couple values and it fails miserably if it is an identity it should not feel even one

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0\[\frac{ 2 }{ 1 + cosx }  \tan^2\frac{ x }{ 2 } = 1\]

xapproachesinfinity
 one year ago
Best ResponseYou've already chosen the best response.2ah wow why you didn't correct me above i was dividing tan^2 over 2 2 was supposed to be within tan

xapproachesinfinity
 one year ago
Best ResponseYou've already chosen the best response.2darn you made me work really hard lol

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0im sorry i wouldve if i known it was wrong but i was confused on this entire problem hence why i am here asking for help

xapproachesinfinity
 one year ago
Best ResponseYou've already chosen the best response.2here what you can do \[\frac{2}{1+\cos x}=1+\tan^2(x/2)=\sec^2(x/2)\] if you prove the left is sec^2(x/2) then you are done!

xapproachesinfinity
 one year ago
Best ResponseYou've already chosen the best response.2that is the same as proving \[\frac{1+\cos x}{2}=\cos^2(x/2) \]

xapproachesinfinity
 one year ago
Best ResponseYou've already chosen the best response.2isn't that some familiar identity to yoou?

xapproachesinfinity
 one year ago
Best ResponseYou've already chosen the best response.2the last line a i wrote should be obvious to you

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0i get it i think the sec and tan identity was what i was thinking i would get to to prove the identity i just wasnt sure how to get there

xapproachesinfinity
 one year ago
Best ResponseYou've already chosen the best response.21+cosx/2=cos^2(x/2) is called half angle identity which can be proven easily but you don't need to draw it all the way as long as that is an identity we know of so the initial problem is an identity as well

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0right right i remember that now

xapproachesinfinity
 one year ago
Best ResponseYou've already chosen the best response.2let's prove that half angle identity for the sake of argument we know that cosx=2cos^2(x/2)1 so 1+cosx=2cos^2(x/2) cos^2(x/2)=(1+cosx)/2 hence proved [cos(2a)=2cos^2a1 is another useful identity]

xapproachesinfinity
 one year ago
Best ResponseYou've already chosen the best response.2they are all linked!

xapproachesinfinity
 one year ago
Best ResponseYou've already chosen the best response.2oh well gotta leave!

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0how do i prove it's sec though?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0@zepdrix I was wondering if you can demonstrate this identity 2/1+cosx  tan^2 x/2=1

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I'm pretty new to this myself, so I'm trying to understand what @xapproachesinfinity did but I think I'm kinda lost...

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.1Mmm can we do it in a new thread? :D I don't feel like reading through all of these comments XD lol

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0mm I pretty much a noob in trig identity LOL but ok xD

xapproachesinfinity
 one year ago
Best ResponseYou've already chosen the best response.2@Learner1298 we already proved it? why you need to prove sec lol read through what i did

Loser66
 one year ago
Best ResponseYou've already chosen the best response.0\[\dfrac{2}{1+cos (x) }tan^2(x/2)\] \[= \dfrac{2}{1+cos(x)} \dfrac{sin^2(x)}{(1+cos (x))^2}\] because \(tan (x/2) = \dfrac{sin (x) }{1+cos x}\)

Loser66
 one year ago
Best ResponseYou've already chosen the best response.0hence, it turns to \(\dfrac{2(1+cos(x)sin^2(x)}{(1+cos(x))^2}\) Now, numerator only:

Loser66
 one year ago
Best ResponseYou've already chosen the best response.0\(2(1+ cos(x) ) sin^2(x)\\=2+2cosx(1cos^2(x) =2+2cos(x)1+cos^2(x) \\=1+2cos(x) +cos^2(x) = (1+cos(x))^2 \)

Loser66
 one year ago
Best ResponseYou've already chosen the best response.0Put it back to the fraction above, we can see that numerator = denorminator , hence the fraction =1 = R H S

Loser66
 one year ago
Best ResponseYou've already chosen the best response.0@xapproach.... hey kid, the second reader didn't understand your stuff. Let old man helps you out. hahahaha.....................

xapproachesinfinity
 one year ago
Best ResponseYou've already chosen the best response.2you did a different version lol this trig stuff there are often many diff ways of doing stuff
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