h, 8cos^4x = 1+ cos4x
<=> 8cos^4x - cos4x = 1

b,

e,

d, sin² 3x + sin² 4x = sin² 5x + sin² 6x,
sin² 3x − sin² 5x = sin² 6x − sin² 4x,
(sin 3x − sin 5x)(sin 3x + sin 5x) = (sin 6x − sin 4x)(sin 6x + sin 4x),
2 sin (−x) cos 4x · 2 sin 4x cos x = 2 sin x cos 5x · 2 sin 5x cos x,
−2 sin x cos x · 2 sin 4x cos 4x = 2 sin x cos x · 2 sin 5x cos 5x,
−sin 2x sin 8x = sin 2x sin 10x,
sin 2x (sin 8x + sin 10x) = 0,
2 sin 2x sin 9x cos x = 0.
=> sin 2x = 0,
x₁ = ½πn (n ∈ ℤ).
hoặc
=> sin 9x = 0,
x₂ = ¹⁄₉πk (k ∈ ℤ).

f,
cos^2 x + cos^2(2x) + cos^2(3x) + cos^2(4x) = 2
<=>1+cos 2x + 1+ cos 4x + 1+ cos 6x + 1 + cos 8x = 4 ( hạ bậc)
<=> ( cos 2x + cos 8x) + ( cos 4x + cos 6x) = 0
<=> 2cos 5x.cos 3x + 2cos 5x. cos x = 0
<=> 2cos 5x. ( cos 3x + cos x) = 0
<=> 4cos 5x. cos 2x. cos x = 0
<=> cos 5x = 0 hoặc cos 2x = 0 hoặc cos x = 0

a, sin4x.sin5x + sin4x.sin3x - sin2x.sinx = 0 
<=> 2sin2x.cos2x.sin5x + 2sin2x.cos2x.sin3x - sin2x.sinx = 0 
* sin2x = 0 <=> x = kpi/2 
* 2sin5x.cos2x + 2sin3x.cos2x - sinx = 0 <=> sin7x + sin3x + sin5x + sinx - sinx = 0 
<=> 2sin5x.cos2x + sin5x = 0 
[ sin5x = 0 --------- [ x = kpi/5 
[ cos2x = -1/2 <=> [ x = ± pi/3 + kpi 

c,