# sin and cosine identity!

• Apr 25th 2006, 06:45 PM
CONFUSED_ONE
sin and cosine identity!
http://i10.photobucket.com/albums/a1...oOkIe/MaTH.jpg

help please! i think the pathagoream[sp*] theorem is used here but i don't know where.
• Apr 25th 2006, 07:09 PM
ThePerfectHacker
Quote:

Originally Posted by CONFUSED_ONE
http://i10.photobucket.com/albums/a1...oOkIe/MaTH.jpg

help please! i think the pathagoream[sp*] theorem is used here but i don't know where.

This is not really an a problem about solve for x,because any makes it true! This is called an identity problem.
You need to demonstrate.
$\cos^2x-\sin^2x=2\cos^2x-1$
By Pythagorean Identity you have that,
$\sin^2x=1-\cos^2x$
Thus, (watch those signs :eek: )
$\cos^2x-(1-\cos^2x)=2\cos^2x-1$
Thus, we have on Left Hand Side,
$2\cos^2x-1=2\cos^2x-1$
(Note I change the name of this thread for reasons explained above).

$\mathbb{Q}.\mathbb{E}.\mathbb{D}$
• Apr 25th 2006, 07:32 PM
CONFUSED_ONE
thank you thank you thank you ThePerfectHacker!
so i see, it's an idenity problem. haha, you changed the title. thanks.
so you substitue the sin^2X to get 1-cos^2X. i see now. thank you again.
:D