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

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

Prove that: 3(sin x-cos x)^(4)+4(sin^(6)x+cos^(6)x)+6(sin x+cos x)^(2)=13

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

If sin^(4)2x+cos^(4)2x=sin2x*cos2x then x=

If sin^(2)4x+cos^(2)x=2sin4x cos^(2)x, then

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

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

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

If sin x+cos x=a then prove that: sin^(6)x+cos^(6)x=1-(3)/(4)(a^(2)-1)^(2), where a^(2)<=2

If sin x+cos x=a, then prove that: sin^(6)x+cos^(6)x=1-(3)/(4)(a^(2)-1)^(2) where a^(2)<=2