Complicated Trigo Identity

Hi Guys,

Am Stuck with this few trigo identtes for days !

1) Prove Identity 1-[ (sinx)^6 + (cosx)^6 ] = 3/4(sin2x)^2

2) Prove Identity (sin2x)^2 [ (cotx)^2 - (tanx)^2 ] = 4cos2x

3) If cosec2x + cot2x = cotx , prove that cosec2x + cosec4x + cosec8x = cotx -cot8x

4) Prove that cosx + cos(x+120) + cos (x+240) = 0

5) Prove that sinx[sin(x+120)] + sinx[sin(x-120)] + [sin(x+120)sin(x-120)] = -3/4

6) Prove that [sin(x-120)]^2 + (sinx)^2 + [sin(x+120)]^2 = 3/2

Please help guys thanks alot !