Hi 100 points to him who has brains and skillz — General Discussion

Forrest 21 Apr 2002, 01:36

Hi guys,

Long time no post. I used to post as a guy named "Beldaran" but my account got totally messed up and I couldn't log in anymore, and it wouldn't send me my password. So I quit waiting for some one to fix it and I just re-registered. Oh well.

Anyways, I have a really hard extra credit math question that I'm stuck on. Can anyone figure this out? (Glenn? Come one, big guy I need you on this one...)

Prove the following identity:

cos(a-b) * cos(a+b) = cos^2a - sin^2b

where "a" and b" are meant as angles "alpha" and "beta" and, even though its not important, are in radians.

I've so far reduced it down to:

cos^2a*cos^2b - sin^2a*sin^2b = cos^2a - sin^2b

I'm pretty much stuck. Whoever gets it figured out should get some major brain points.

PS - Nice to see you folks again.😊

Cyclone 21 Apr 2002, 01:46

Hi Beldaran, maybe WL will be able to help you with your old account. LEt's hope so. :thumbsup:

And I have both good news and bad news. The good news is that I've seen this before.

The bad news is that I was never that skilled with sines, cosines, and the like. :shrug:

Glenn? 😊

Cyclone

Forrest 21 Apr 2002, 01:50

Hi nice to see you again Cyclone.

Yeah, its a tuffy. I've been staring at it long enough to where I know I'm just in a rut and won't get anywhere. I'm going to go do something else.

I would, of course, still like to hear form anyone who may have insight on it.

DarkDragon 21 Apr 2002, 02:08

Yes, no problem.
cos(a-b) * cos(a+b) = cos(a)^2 - sin(b)^2
(cos(a)cos(b)+sin(a)sin(b))*(cos(a)cos(b)-sin(a)sin(b)) = cos(a)^2 - sin(b)^2
cos(a)^2 * cos(b)^2 - sin(a)^2 * sin(b)^2 = cos(a)^2 - sin(b)^2

Since sin^2 + cos^2 = 1,

cos(a)^2 * (1-sin(b)^2) - (1 - cos(a)^2)sin(b)^2 = cos(a)^2 - sin(b)^2
cos(a)^2 - cos(a)^2 * sin(b)^2 - sin(b)^2 + sin(b)^2 * cos(a)^2 = cos(a)^2 - sin(b)^2
cos(a)^2 - sin(b)^2 = cos(a)^2 - sin(b)^2

Forrest 21 Apr 2002, 02:25

Damn it! I knew I was overlooking one tiny little thing. I always do that. All I had to do was realize cos^2 = 1-sin^2

Thanks DarkDragon. You're the man of the hour by far.😊

Dechipher 21 Apr 2002, 02:28

HEy belderan!!! Long time no see...

Forrest 21 Apr 2002, 02:29

'sup decipher?

How's life treating you? Did I miss anything really juicy while I was away?

PS- I'm digging the "Hyrule Night" style set:thumbsup:

Tygore 21 Apr 2002, 03:11

Oh, you're beldaran?
Is your first name really Forrest?
Are you my dad?

GameQueen 21 Apr 2002, 03:34