# Prove this identity?

• Apr 5th 2010, 03:32 PM
dlngoal
Prove this identity?
Can someone please help me solve this identity? I need all steps. I really just do not understand it :/

thank you !

sin^4 β - cos^4 β = 1 - 2cos^2 β
• Apr 5th 2010, 04:39 PM
dlngoal
I mean *PROVE this identity.
using trigonometric identities :|
• Apr 5th 2010, 05:15 PM
harish21
Quote:

Originally Posted by dlngoal
Can someone please help me solve this identity? I need all steps. I really just do not understand it :/

thank you !

sin^4 β - cos^4 β = 1 - 2cos^2 β

$\displaystyle (sin^{4}\beta) - (cos^{4}\beta)$

$\displaystyle = {(sin^{2}\beta)^2} -{(cos^{2}\beta)^2}$

$\displaystyle = (sin^{2}\beta + cos^{2}\beta) \times (sin^{2}\beta - cos^{2}\beta)$ [ $\displaystyle Note: (a^2-b^2) = (a+b)(a-b)$ ]

$\displaystyle = 1 \times (sin^{2}\beta - cos^{2}\beta)$ [$\displaystyle Note: sin^{2}x+cos^{2}x = 1$]

$\displaystyle = [(1-cos^{2}\beta) -cos^{2}\beta]$ $\displaystyle [Note: sin^{2}x = 1 - cos^{2}x$]

$\displaystyle = 1 - 2cos^{2}\beta$
• Apr 5th 2010, 05:20 PM
dlngoal
You are a life saver thank youu
• Apr 5th 2010, 05:23 PM
harish21
Quote:

Originally Posted by dlngoal
You are a life saver thank youu

haha! Am I really?
• Apr 5th 2010, 05:29 PM
dlngoal
Yess! You are! haha