Cosxcos2xcos4xcos8xcos16x=sin32x/32sinx доказать тождество

Question

Cosxcos2xcos4xcos8xcos16x=sin32x/32sinx доказать тождество

Answer 1

                                          Решение:

умножим и разделим на 2sinx
2sinxcosxcos2xcos4xcos8xcos16x/2sinx=2sin2xcos2xcos4xcos8xcos16x/4sinx=
=sin4xcos4xcos8xcos16x/4sinx=sin8xcos8xcos16x/8sinx=2sin16xcos16x/16sinx=
=sin16xcos16x/16sinx=sin32x/32sinx.