Question

prove that cos x cos 2x cos 4x cos 8x =sin 16x/16 sin x

Answer 1

Here we use sin 2x = 2sinx Cosx formula 4 times

Answer 2

Answer:

To prove: cos x × cos 2x × cos 4x × cos 8x = (sin 16x)/(16 × sin x)

Consider,

LHS

= cos x × cos 2x × cos 4x × cos 8x

$=\frac{2\times sin\,x\times cos\,x\times cos\,2x\times cos\,4x\times cos\,8x}{2\times sin\,x}$

$=\frac{sin\,2x\times cos\,2x\times cos\,4x\times cos\,8x}{2\times sin\,x}$

$=\frac{2\times sin\,2x\times cos\,2x\times cos\,4x\times cos\,8x}{2\times2\times sin\,x}$

$=\frac{sin\,4x\times cos\,4x\times cos\,8x}{4\times sin\,x}$

$=\frac{2\times sin\,4x\times cos\,4x\times cos\,8x}{2\times4\times sin\,x}$

$=\frac{sin\,8x\times cos\,8x}{8\times sin\,x}$

$=\frac{2\times sin\,8x\times cos\,8x}{2\times8\times sin\,x}$

$=\frac{sin\,16x}{16sin\,x}$

= RHS

Hence  Proved