sinα1sinα2sinα3...sinαn Multiplying both sides by sinα1sinα2sinα3,...sinαn ⇒sin2α1sin2α2sin2α3...sin2αn =(sinα1cosα1)(sinα2cosα2) ⇒sin2α1sin2α2sin2α3...sin2αncosαn) =
1
2n
(sin2α1)(sin2α2)...(sin2αn) As we know maximum value of sinθ is 1 ⇒sin2α1sin2α2sin2α3...sin2αn≤