Answers

2014-08-17T07:16:18+05:30
Remember : 2 sin(p) cos(p) = sin(2p)
Let,
A = cos(x) cos(2x) cos(4x) cos(8x)
2 sin(x) A = 2 sin(x) cos(x) cos(2x) cos(4x) cos(8x)
2 sin(x) A = sin(2x) cos(2x) cos(4x) cos(8x)
4 sin(x) A = 2 sin(2x) cos(2x) cos(4x) cos(8x)
4 sin(x) A = sin(4x) cos(4x) cos(8x)
8 sin(x) A = 2 sin(4x) cos(4x) cos(8x)
8 sin(x) A = sin(8x) cos(8x)
16 sin(x) A = 2 sin(8x) cos(8x)
16 sin(x) A = sin(16x)

A =  \frac{sin(16x)}{16 sin(x)}

And, 16 =  4^{2} \\ 4 =  2^{2}  \\ 16 =  ( 2^{2} )^{2}

Replacing 16 in terms of powers of 2

A =  \frac{sin(( 2^{2} )^{2}x)}{( 2^{2} )^{2}sin(x)} \\  \\ cos(x) cos(2x) cos(4x) cos(8x) =  \frac{sin(( 2^{2} )^{2}x)}{( 2^{2} )^{2}sin(x)}
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