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

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- Apr 5th 2010, 03:32 PMdlngoalProve 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 PMdlngoal
I mean *PROVE this identity.

using trigonometric identities :| - Apr 5th 2010, 05:15 PMharish21
$\displaystyle (sin^{4}\beta) - (cos^{4}\beta)$

$\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 PMdlngoal
You are a life saver thank youu

- Apr 5th 2010, 05:23 PMharish21
- Apr 5th 2010, 05:29 PMdlngoal
Yess! You are! haha