[faithHunter]

I now realize how mathemathically less inclined I am compared to the rest of you guys now after reading through this thread.

I don't even get half the terms that you are using :P

Quick Comments

	mGGNemesis:	lol poor faith; dw :)
	RVLiveR:	it's okay, everything is equal to 1 if 1+1=1
	AxS.Sorathez:	If 1+1=1 then anything and everything is true :D

[AxS.pinealan]

Hey I got a trigonometry question for you guys:
Use mathematical induction to prove that for any positive integer n,
sinx+sin3x+...+sin(2n-1)x= (1-cos2nx)/2sinx
where sinx =/= 0

[Mukade]

Originally Posted by pinealan

Hey I got a trigonometry question for you guys:
Use mathematical induction to prove that for any positive integer n,
sin x+sin 3x+...+sin(2n-1)x= (1-cos2nx)/2sin x
where sin x =/= 0

I'll use the indentity (1) (sin x)^2= (1-cos 2x)/2
because (sin nx)^2/(sin x) is easier to work with.
and also use
(2) (sin A sin B=1/2(cos(A-B)-cos(A+B))


Set n=1

lhs=sinx
rhs=(sin x)^2/sin x
=sin x
=lhs
true for n=1

Assume n=k
sin x+ sin 3x+...+sin(2k-1)x=(sin kx)^2/(sin x)

For n=k+1

lhs= ((sin kx)^2)/sin x+sin(2k+1)x
=(((sin kx)^2)+sin(2k+1)x sin x)/sin x
=(((sin kx)^2)+1/2(cos(x-2kx-x)-cos(2kx+2x))/sin x (2)
=(((sin kx)^2)+1/2(cos(-2kx)-cos(2kx+2x))/sin x
=(((sin kx)^2)+1/2(cos(2kx)-cos(2kx+2x))/sin x
=((((sin kx)^2)+1/2(1-2(sin kx)^2-(1-2(sinkx+x))^2))/sin x
=((((sin kx)^2)+1/2(2(sin kx+x))^2-2(sin kx)^2))/sin x
=((sin kx)^2+(sin kx+x))^2-(sin kx)^2)/sin x
=(sin(k+1)x)/sin x
=rhs

Therefore, true for all n.

[Mukade]

Admittedly, I've done this question before and still have the textbook worked solution >.>

Quick Comments

syfPhoenix:

Knew it was too good to be true. :P

[AuXCoolpuff]

I don't want to live on this planet any more.

Quick Comments

	Mukade:	Lololol
	mGGNemesis:	lolol

[|Erasmus|]

You Tube

You Tube

Quick Comments

Mukade:

This is amazing

[Zepph]

I could fap to this thread.

Maths .

Quick Comments

	Maynarde:	NERD
	TheGentleman:	@Maynerd: And don't you forget it!!
	RVLiveR:	zepph is my new best friend~ ^.^

[TheGentleman]

I know this probably belongs in the puns thread but... I'm so glad this thread exists.

I wish you were sine^2 and I was cosine^2 so together we could be 1

Quick Comments

	Mukade:	Cute as bro :P
	AxS.pinealan:	lol nice pun, never have thought of that before
	AxS.Sorathez:	I love it :D You can always be my Cos^2
	mGGNemesis:	awwww nice <3

[AxS.pinealan]

Well, frankly, I pulled that question from my textbook too :P

[AxS.Sorathez]

Originally Posted by Mukade

I'll use the indentity (1) (sin x)^2= (1-cos 2x)/2
because (sin nx)^2/(sin x) is easier to work with.
and also use
(2) (sin A sin B=1/2(cos(A-B)-cos(A+B))


Set n=1

lhs=sinx
rhs=(sin x)^2/sin x
=sin x
=lhs
true for n=1

Assume n=k
sin x+ sin 3x+...+sin(2k-1)x=(sin kx)^2/(sin x)

For n=k+1

lhs= ((sin kx)^2)/sin x+sin(2k+1)x
=(((sin kx)^2)+sin(2k+1)x sin x)/sin x
=(((sin kx)^2)+1/2(cos(x-2kx-x)-cos(2kx+2x))/sin x (2)
=(((sin kx)^2)+1/2(cos(-2kx)-cos(2kx+2x))/sin x
=(((sin kx)^2)+1/2(cos(2kx)-cos(2kx+2x))/sin x
=((((sin kx)^2)+1/2(1-2(sin kx)^2-(1-2(sinkx+x))^2))/sin x
=((((sin kx)^2)+1/2(2(sin kx+x))^2-2(sin kx)^2))/sin x
=((sin kx)^2+(sin kx+x))^2-(sin kx)^2)/sin x
=(sin(k+1)x)/sin x
=rhs

Therefore, true for all n.

I had quite the love/hate relationship with mathematical induction in High School...

[TheGentleman]

Originally Posted by pinealan

Well, frankly, I pulled that question from my textbook too :P

Now now... we won't do your homework for you!

[|Erasmus|]

And here's what we all want math to be:

+ Show +

Quick Comments

ToRSpartaz:

MAAAAAAAAAAAAAAAATH

[ToRSpookToR]

[6:50:21 AM] Nick "ToRSpartaz" Simpson: 10 + - 11 is 21

Quick Comments

Mukade:

Pure genius

[ToRSpartaz]

In my defense, I only woke up a few minutes before that comment...

Quick Comments

mGGNemesis:

lolol

[mGGNemesis]

I this thread

Quick Comments

Mukade:

:)

[ToRSpartaz]

Love Math, hate proofs T_T, proofs make me die a little inside

Quick Comments

	ToRLuneth:	So does basic arithmetic it seems <3
	ToRSmotPokingFish:	this^^

[Antel0pe]

Wait, so i can scan sheets of my homework in, and people will just answer it yeh? ^.^
I approve of this thread

Quick Comments

	|Erasmus|:	no.
	ToRsupapower:	no.
	Mukade:	I might. I promise I won't answer them wrong
	mGGPrometheus:	I probably would
	RVLiveR:	mm koreans asking for help at math..
	mGGNemesis:	anyone could... though I'm not sure about trusting the answers ;)

[RVLiveR]

yo guys for anybody who will be at the coming SEAMC you should greet me ^.^ I'll be in the JIS A-Team with two koreans so I'll stand out :P

[Antel0pe]

Originally Posted by Antelopes

*sRLiveR: *
mm koreans asking for help at math..

Wow, that stereotype T_T.
I'm Wood League in Math ;_;

[AxS.pinealan]

Originally Posted by Antelopes

Wow, that stereotype T_T.
I'm Wood League in Math ;_;

You mean Korean wood league? Thats NA Masters

Quick Comments

	Mukade:	Lolololol
	syfPhoenix:	I lol'd a little.