Prove that `cos^(4)x-sin^(4)x=cos^(2)x-sin^(2)x`

Prove that :cos4x=1-8sin^(2)x cos^(2)x

Prove that sin^(4)x-cos^(4)x=sin^(2)x-cos^(2)x

Prove that sin^(4)x-cos^(4)x=sin^(2)x-cos^(2)x

sin^(4)x-cos^(4)x=sin^(2)x-cos^(2)x

sin^(4)x-cos^(4)x=sin^(2)x-cos^(2)x

prove that cos^(3)(2x)+3cos2x=4(cos^(6)x-sin^(6)x)

Prove that: cos^(2)2x-cos^(2)6x=sin4x sin8x

If y=(sin^(4)x-cos^(4)x+sin^(2) x cos^(2)x)/(sin^(4) x+ cos^(4)x + sin^(2) x cos^(2)x), x in (0, pi/2) , then

Solev (sin^(2) 2x+4 sin^(4) x-4 sin^(2) x cos^(2) x)/(4-sin^(2) 2x-4 sin^(2) x)=1/9 .

sin^(4)x+cos^(4)x=1-2sin^(2)x cos^(2)x