Вычислить: cos15п/32 * cos п/32 * cos п/16 * cos п/8

Question

Вычислить: cos15п/32 * cos п/32 * cos п/16 * cos п/8

Answer 1

Cos15π/32=cos(π/2-π/32)=sinπ/32
sinπ/32*cosπ/32*cosπ/16*cosπ/8=1/2*sinπ/16*cosπ/16*cosπ/8=
=1/4sinπ/8*cosπ/8=1/8*sinπ/4=1/8*√2/2=√2/16