The value of cos π65 cos 2π65 cos 4π65 cos 8π65 cos 16π65 cos 32π65 is
none of these
We have,
cos π65 cos 2π65 cos 4π65 cos 8π65 cos 16π65 cos 32π65
=2 sinπ652 sin π65 cos π65 cos 2π65 cos 4π65 cos 8π65 cos 16π65 cos 32π65
(dividing and multiplying by 2 sin π65)
=2 sin2π652×2 sin π65 cos 2π65 cos 4π65 cos 8π65 cos 16π65 cos 32π65=2 sin4π652×4 sin π65 cos 4π65 cos 8π65 cos 16π65 cos 32π65=2 sin8π652×8 sin π65 cos 8π65 cos 16π65 cos 32π65=2 sin16π652×16 sin π65 cos 16π65 cos 32π65=2 sin32π652×32 sin π65 cos 32π65
=sin64π6564 sin π65=sin(π−π65)64 sin π65=sinπ6564 sin π65=164