LHS=(2sinAcosAcos2Acos4Acos8A2sinA)=(2×sin2Acos2Acos4Acos8A2×2sinA)=(2×sin4Acos4Acos8A2×4sinA)=(2×sin8Acos8A2×8sinA)=(sin16A16sinA)=RHS
Prove that cos A 2A cos 4A cos 8A = sin 16A16 sin A.