8sin(π/32)cos(π/32)cos(π/16)cos(π/8),求值
问题描述:
8sin(π/32)cos(π/32)cos(π/16)cos(π/8),求值
答
8sin(π/32)cos(π/32)cos(π/16)cos(π/8),
=4sinπ/16cos(π/16)cos(π/8),
=2sin(π/8)cos(π/8)
=sin(π/4)
=√2/2
答
运用公式sin2α=2sinαcosα8sin(π/32)cos(π/32)cos(π/16)cos(π/8)=4×2sin(π/32)cos(π/32)cos(π/16)cos(π/8)=4×sin(π/16)cos(π/16)cos(π/8)=2×2sin(π/16)cos(π/16)cos(π/8)=2sin(π/8)cos(π/8)=si...