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