Prove Trig Identity

Sep 2016
66
0
Muskoka
trigIdent.png
How do you solve this? I brought it down to (cos^4(x) -sin^4(x))=cos(2x)+2sin^4(x) but I don't know how to continue
 
Dec 2014
129
101
USA
$\cos^8{x}-\sin^8{x} $

$(\cos^4{x}-\sin^4{x})(\cos^4{x}+\sin^4{x})$

$(\cos^2{x}+\sin^2{x})(\cos^2{x}-\sin^2{x})(\cos^4{x}+\sin^4{x})$

$(1)[\cos(2x)][(1-\sin^2{x})^2 + \sin^4{x})]$

$\cos(2x)[(1-2\sin^2{x})+2\sin^4{x}]$

$\cos(2x)[\cos(2x)+2\sin^4{x}]$

$\cos^2(2x) + 2\cos(2x)\sin^4{x}$
 
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