Question

solve for x: Sqrt(1+cosX) - Sqrt(2)cos(x/2) = Sqrt(2)

Answer 1

\[\sqrt{1+\cos(x)} -\sqrt{2\cos\left(\frac{x}{2}\right)} = \sqrt{2}\]Is this your question?

Answer 2

ill post the question, but i bealive it is (Sqrt 2) cos........

Answer 3

number 3

Answer 4

believe*

Answer 5

@Jhannybean

Answer 6

Ah, it is: \(\sqrt{1+cos(\theta)}-\sqrt{2}\cos\left(\frac{\theta}{2}\right)=\sqrt{2}\)

Answer 7

yup, would you be able to to briefly explain the process

Answer 8

i'm trying to solve it myself first :) one minute.

Answer 9

ok this is what someone posted yesterday and didnt explain anything http://openstudy.com/study#/updates/5483bf86e4b01e7eabcbc938

Answer 10

Yeah I'm not really sure what to do with the middle term, and am kind of confused how to solve it mysle.fI am sorry :(

Answer 11

myself*

Answer 12

its cool, thanks for trying anyway!!

Answer 13

Hmm.. what if we replaced \(\theta\) by \(x\)?

Answer 14

na, its just a place holder. i have to go to work now, if you happen to have a break through, let me know lol

Answer 15

\[\sf \sqrt{1+\cos(\theta)}-\sqrt{2}\cos\left(\dfrac{\theta}{2}\right)=\sqrt{2}\]Lets replace \(\theta\) with \(x\), so our new equation will become :\[\sqrt{1+\cos(x)} -\sqrt{2}\cos\left(\frac{x}{2}\right)=\sqrt{2}\]Add \(+\sqrt{2} \cos\left(\frac{x}{2}\right)\) to both sides. \[\sqrt{1+\cos(x)} = \sqrt{2}+\sqrt{2}\cos \left(\frac{x}{2}\right)\]Square both sides., \[1+\cos(x) =\left(\sqrt{2}+\sqrt{2}\cos\left(\frac{x}{2}\right)\right)^2\]Now expand the right side.

Get back o me when you've gotten this far,

Answer 16

i still dont how to continue, but i did it @Jhannybean

Answer 17

see*

Answer 18

@imyint would you be able to help

Answer 19

What did you get when you expanded the right side?

Answer 20

took e a while, but this problem is a little easier than it looks.

Answer 21

yeah, i got it. i completely missed the half angel id lol there is no solution 0=sqrt(2)

Answer 22

Yeah!! good job :)