# Proving a conditional indentity

• Jul 3rd 2013, 05:40 AM
AaPa
Proving a conditional indentity
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 AM
BobP
Re: Proving a conditional indentity

$\cos \left(\frac{A+B}{2}\right)$ is not equal to $-\cos\left(\frac{C}{2}\right).$
• Jul 3rd 2013, 07:11 AM
AaPa
Re: Proving a conditional indentity
how?
cos[(A+B)/2]
=cos[(pi - c )/2]
= -cos (c/2)
• Jul 3rd 2013, 07:24 AM
BobP
Re: Proving a conditional indentity
$\frac{\pi - C}{2}=\frac{\pi}{2}-\frac{C}{2}.$
• Jul 3rd 2013, 07:35 AM
AaPa
Re: Proving a conditional indentity
yes I know that but A+B+C=pi

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

Expand $\cos\left(\frac{\pi}{2}-\frac{C}{2}\right).$
• Jul 3rd 2013, 08:30 AM
AaPa
Re: 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 AM
HallsofIvy
Re: Proving a conditional indentity
Well, sin(c/2) is certainly NOT equal to -cos(c/2)!
• Jul 3rd 2013, 09:14 AM
BobP
Re: Proving a conditional indentity
You can't without introducing a square root, instead replace the $\cos ^{2}\left(\frac{C}{2}\right)$ by $1-\sin ^{2}\left(\frac{C}{2}\right).$
• Jul 3rd 2013, 09:47 AM
AaPa
Re: 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 AM
BobP
Re: Proving a conditional indentity
The second line is wrong.
Read again posts 4 and 6.
• Jul 3rd 2013, 06:09 PM
AaPa
Re: Proving a conditional indentity
Okay i got it.

thanks.
• Jul 3rd 2013, 08:40 PM
ibdutt
Re: Proving a conditional indentity