Yahoo Answers is shutting down on May 4th, 2021 (Eastern Time) and beginning April 20th, 2021 (Eastern Time) the Yahoo Answers website will be in read-only mode. There will be no changes to other Yahoo properties or services, or your Yahoo account. You can find more information about the Yahoo Answers shutdown and how to download your data on this help page.
Trending News
Prove the identity: cos(x+x) = cos^2(x) - sin^2(x)?
This is a slam dunk from the addition of cosines law. How do you derive THAT? Thanks!
6 Answers
- sofarsogoodLv 51 decade agoFavorite Answer
I tried to do it with minimal drawings and it is hard to describe. This website has it in detail (with drawings): http://mathforum.org/library/drmath/view/54051.htm...
- Jim BurnellLv 61 decade ago
Nah, it doesn't need to be as hard as Ramzi made it.
It's just an application of the formula for the cosine of the sum of two angles.
cos(a + b) = cosa cosb - sina sinb
cos(x + x) = cosx cosx - sinx sinx = cos^2x - sin^2x
It's that easy.
----
Edit: I've never tried to prove the formula itself, but I found a derivation here:
Source(s): http://www.phy6.org/stargaze/Strig5.htm http://whyslopes.com/etc/CalculusAndBeyond/ch23a.h... - averagebearLv 61 decade ago
Are you proving from cos x = (e^{ix}+e^{-ix})/2, or power series? Not sure what level proof you need here.
- 1 decade ago
cos(x+x)=cosx*cosx-sinx*sinx
=cos^2(x)-sin^2(x)
it comes from cos(a+b)=cosa*cosb-sina*sinb
solved!!!
- How do you think about the answers? You can sign in to vote the answer.
- 1 decade ago
cos^2(x) = .5 + cos(2x)/2
sin^2(x) = .5 - cos(2x)/2
cos(x+x) = cos(2x)
cos^2(x) - sin^2(x) = 5 + cos(2x)/2 - (.5 - cos(2x)/2) = 2cos(2x)/2 = cos(2x)
- Professor MaddieLv 41 decade ago
cos(x+x)=cos(x)cos(x) - sin(x)sin(x) from the sum formula of the cosine:
cos(u+v)=cos(u)cos(v)-sin(u)sin(v)
Source(s): Here's a derivation: http://homepage.mac.com/shelleywalsh/MathArt/Cosin...