compound angle formulae

(sorry, my iPad can't type theta, so I use 'x')
cos x cos 2x cos 4x = 2 cos^2 x - cos x
cos x cos 2x (1 - 2 sin^2 2x) = cos x (2 cos^2 - 1)
cos x cos 2x - 2 cos x cos 2x sin 2x sin 2x = cos x cos 2x
cos x sin 2x sin 4x = 0
cos x = 0 or sin 2x = 0 or sin 4x = 0
x = n (pi/4) . . . where n is an integer

2012-09-17 20:03:55 補充：
Sorry, typo error, the second line is 'to the power of 3' instead of '2'.

2012-09-17 21:40:11 補充：
I assume you are talking about 2 terms,
(i) cos x cos 2x cos 4x
(ii) 2 cos^3 x - cos x
Are (i), (ii) the same ?

As I show you before,
(ii) = cos x (2 cos^2 x - 1) = cos x cos 2x
So, one is (cos x cos 2x cos 4x), and the other is (cos x cos 2x).
Obviously, they are not the same unless cos 4x = 1

R.H.S =2 cos^3 θ - cosθ

= cosθ(2cos^2 θ -1)

= cosθ(cos2θ)

therefore R.H.S # L.H.S , except cos4θ = 1 or cosθ= 0


希望幫到你!

2012-09-22 16:54:00 補充：
or cos2θ = 0

Put x = 30
cos 30 cos 60 cos 120 = - (sqrt 3)/8
2 cos 30 cos 30 cos 30 - cos 30 = (sqrt 3)/4
so they are not the same.