# Thread: Prove this identity?

1. ## 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

2. I mean *PROVE this identity.
using trigonometric identities :|

3. 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
$\displaystyle (sin^{4}\beta) - (cos^{4}\beta)$

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

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

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

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

$\displaystyle = 1 - 2cos^{2}\beta$

4. You are a life saver thank youu

5. Originally Posted by dlngoal
You are a life saver thank youu
haha! Am I really?

6. Yess! You are! haha