Please see the attached image.

I need to prove a conditional identitycosA + cosB + cosC = 1 + 4sin(A/2) + sin(B/2) + sin(C/2)

given that A+B+C=pi. But the negative sign at the last is giving me trouble.

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- Jul 3rd 2013, 05:40 AMAaPaProving a conditional indentity
Please see the attached image.

I need to prove a conditional identity**cosA + cosB + cosC = 1 + 4sin(A/2) + sin(B/2) + sin(C/2)**

given that A+B+C=pi. But the negative sign at the last is giving me trouble. - Jul 3rd 2013, 06:40 AMBobPRe: Proving a conditional indentity
Your mistake is on your second line.

$\displaystyle \cos \left(\frac{A+B}{2}\right)$ is not equal to $\displaystyle -\cos\left(\frac{C}{2}\right).$ - Jul 3rd 2013, 07:11 AMAaPaRe: Proving a conditional indentity
how?

cos[(A+B)/2]

=cos[(pi - c )/2]

= -cos (c/2) - Jul 3rd 2013, 07:24 AMBobPRe: Proving a conditional indentity
$\displaystyle \frac{\pi - C}{2}=\frac{\pi}{2}-\frac{C}{2}.$

- Jul 3rd 2013, 07:35 AMAaPaRe: Proving a conditional indentity
yes I know that but A+B+C=pi

so A+B=pi-c - Jul 3rd 2013, 07:45 AMBobPRe: Proving a conditional indentity
!!!!!!!

Expand $\displaystyle \cos\left(\frac{\pi}{2}-\frac{C}{2}\right).$ - Jul 3rd 2013, 08:30 AMAaPaRe: Proving a conditional indentity
i know that it is equal to sin(c/2) but i want to write it in the form of cos.

- Jul 3rd 2013, 09:11 AMHallsofIvyRe: Proving a conditional indentity
Well, sin(c/2) is certainly NOT equal to -cos(c/2)!

- Jul 3rd 2013, 09:14 AMBobPRe: Proving a conditional indentity
You can't without introducing a square root, instead replace the $\displaystyle \cos ^{2}\left(\frac{C}{2}\right)$ by $\displaystyle 1-\sin ^{2}\left(\frac{C}{2}\right).$

- Jul 3rd 2013, 09:47 AMAaPaRe: Proving a conditional indentity
cos[(pi-c)/2]

=cos(-c/2)

=-cos(c/2)

at which step am I wrong? - Jul 3rd 2013, 11:30 AMBobPRe: Proving a conditional indentity
The second line is wrong.

Read again posts 4 and 6. - Jul 3rd 2013, 06:09 PMAaPaRe: Proving a conditional indentity
Okay i got it.

thanks. - Jul 3rd 2013, 08:40 PMibduttRe: Proving a conditional indentity