# Prove Trig Identity

#### Ilikebugs

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

#### Cervesa

$\cos^8{x}-\sin^8{x}$

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

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

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

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

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

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

topsquark