$\cos\dfrac{x}{5}.\cos\dfrac{2x}{5}.\cos\dfrac{4x}{5}.\cos\dfrac{8x}{5}$
$=\dfrac{\sin\dfrac{x}{5}.\cos\dfrac{x}{5}.\cos\dfrac{2x}{5}.\cos\dfrac{4x}{5}.\cos\dfrac{8x}{5} }{\sin\dfrac{x}{5}}$
$=\dfrac{\dfrac{1}{2}.\sin\dfrac{2x}{5}\cos\dfrac{4x}{5}.\cos\dfrac{8x}{5}}{\sin\dfrac{x}{5}}$
$=\dfrac{\dfrac{1}{4}.\sin\dfrac{4x}{5}.\cos\dfrac{4x}{5}.\cos\dfrac{8x}{5}}{\sin\dfrac{x}{5}}$
$=\dfrac{\dfrac{1}{8}.\sin\dfrac{8x}{5}.\cos\dfrac{8x}{5}}{\sin\dfrac{x}{5}}$
$=\dfrac{\sin\dfrac{16x}{5}}{16\sin\dfrac{x}{5}}$
