Prove this identity?

**dlngoal** · April 5th 2010, 03:32 PM

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

**dlngoal** · April 5th 2010, 04:39 PM

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

**harish21** · April 5th 2010, 05:15 PM

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

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

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

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

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

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

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

**dlngoal** · April 5th 2010, 05:20 PM

You are a life saver thank youu

**harish21** · April 5th 2010, 05:23 PM

Originally Posted by dlngoal

You are a life saver thank youu

haha! Am I really?

**dlngoal** · April 5th 2010, 05:29 PM

Yess! You are! haha

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