Prove that \(\frac { 4tan\ x(1-{ tan }^{ 2 }x) }{ 1-6{ tan }^{ 2 } x+{ tan }^{ 4 } x } =tanx\)

Prove that (sin 3x + sin x) sin x + (cos 3x - cos x) cos x = 0.

Prove that sin(n+1)x sin(n+2) x+cos(n+1)xcos(n+2)x=cosx.

If tan x = \(\frac { -4 }{ 3 } \) and x is in II quadrant,find \(sin\frac { x }{ 2 } ,cos\frac { x }{ 2 } \) and \(tan\frac { x }{ 2 } \)

Prove that cos²2x - cos²6x = sin 4x.sin 8x