Question

prove that :cosx cos2x cos4x cos8x=sin 16x/16sinx

Answer 1

cosxcos2scos4xcos8x
=1/2sinx[(2sinxcosx)cos2xcos4xcos8x]
=1/2sinx(sin2xcos2xcos4xcos8x)
=1/4sinx[(2sin2xcos2x)cos4xcos8x]
=1/4sinx(sin4xcos4xcos8x)
=1/8sinx[(2sin4xcos4x)cos8x]
=1/8sinx(sin8xcos8x)
=1/16sinx(2sin8xcos8x)
=1/16sinx(sin16x)
=sin16x/16sinx (Proved)

Answer 2

cosxcos2scos4xcos8x

We,will multiple it by 1/2&2 to use C+D identity:

=1/2sinx[(2sinxcosx)cos2xcos4xcos8x]

=1/2sinx(sin2xcos2xcos4xcos8x)

=1/4sinx[(2sin2xcos2x)cos4xcos8x]

=1/4sinx(sin4xcos4xcos8x)

=1/8sinx[(2sin4xcos4x)cos8x]

=1/8sinx(sin8xcos8x)

=1/16sinx(2sin8xcos8x)

=1/16sinx(sin16x)

=sin16x/16sinx