Question

Prove that: cosA. Cos2A. cos4A. cos8A = sin 16 A / 16 sin A

Answer 1

cosAcos2Acos4Acos8A
=(1/2sinA)(2sinAcosAcos2Acos4Acos8A)
=(1/2sinA)(sin2Acos2Acos4Acos8A)
=(1/4sinA)(2sin2Acos2Acos4Acos8A)
=(1/4sinA)(sin4Acos4Acos8A)
=(1/8sinA)(2sin4Acos4Acos8A)
=(1/8sinA)(sin8Acos8A)
=(1/16sinA)(2sin8Acos8A)
=(1/16sinA)(sin16A)
=sin16A/16sinA (Proved)