An Identity

E

evenkeel3x

New member
Joined
Feb 28, 2010
Messages
14
Hello, I need help doing this identity:

(1+cosX)(tanX/2)=sinX

No obvious formulas come to mind, but I've tried to manipulate the tan double angle formula to accomodate X/2.
This is the origional tan double angle formula:
tan(2X)=(2tanX)/(1-tan^2X)

I then tried to divide the right side by four to hopefully equal the tanX/2 value. I don't even know if that's legal.
So now I have:

(1+cosX) ((2tanX)/(1-tan^2X))/4=sinX

And now I'm very wholeheartedly stuck. It's probably something simple I'm missing, but I don't know.
A Quick Response would be greatly appreciated!
Thanks.
 
evenkeel3x said:
Hello, I need help doing this identity:

(1+cosX)(tanX/2)=sinX

What is tanX/2?

Is it 1/2 * tan(X)

or

Is it tan(X/2)?

I have a hunch - but you need to post problems correctly.

Following my hunch -

Hint:

1 + cos(X) = 2 * cos[sup:11hgbp8k]2[/sup:11hgbp8k](X/2)


No obvious formulas come to mind, but I've tried to manipulate the tan double angle formula to accomodate X/2.
This is the origional tan double angle formula:
tan(2X)=(2tanX)/(1-tan^2X)

I then tried to divide the right side by four to hopefully equal the tanX/2 value. I don't even know if that's legal.
So now I have:

(1+cosX) ((2tanX)/(1-tan^2X))/4=sinX

And now I'm very wholeheartedly stuck. It's probably something simple I'm missing, but I don't know.
A Quick Response would be greatly appreciated!
Thanks.
Click to expand...
 
1 + cos(X) = 2 * cos2(x/2)

I understand how you got that, but how does the 2 * cos2(x/2) simplify with the tan(X/2) to make sin(X)?
 
[1+cos x][tan[x/2]] =sin x rewrite in terms of x/2
x=x/2+x/2
tanu=sin u/ cos u
[1+cos[x/2+x/2]][sinx/2] / cos x/2 =
cos [a+b]=cosa cosb-sina sinb
sin[a+b]=sinacosb+cosa sinb
[1+coscosx/2-sinx/2sinx/2][sin x/2] / cosx/2=
[1+cos^2x/2-sin^2x/2][sin x/2 /cos x/2=
[1+1-sin^2 x/2 - sin^2 x/2][sin x/2]/cos x/2=
[2-2sin^2/x/2]sin x/2 / cos x/2=
2[cos^2 x/2]sinx/2/cos x/2=
2cosx/2sinx/2=
sin[x/2+x/2]=
sinx= sin x proof
Arthur
 
evenkeel3x said:
1 + cos(X) = 2 * cos[sup:12b5vj1x]2[/sup:12b5vj1x](x/2)

I understand how you got that, but how does the 2 * cos2(x/2) simplify with the tan(X/2) to make sin(X)?
Click to expand...

use

tan(X/2) = sin(X/2) / cos(X/2)
 
Wow, thanks so much. It took me a while to figure out what that said, but thanks!
~will
 
evenkeel3x said:
Wow, thanks so much. It took me a while to figure out what that said, but thanks!
~will
Click to expand...

Why?

It took you < 2 minutes to figure that out (looking at the post times).
 
I was talking about Arthur's reply. Yours was nicely spaced and easy to read, but it took some deciphering to figure out what he said. Thanks so much for the help though, I really appreciate it. :D
 
You must log in or register to reply here.
Top