sin10sin30sin50sin70 Ответ 0.0625, нужно подробное решение.

Question

sin10sin30sin50sin70

Ответ 0.0625, нужно подробное решение.

Answer 1

sin10sin30sin50sin70=cos10sin10sin30sin50sin70/cos10=
=1/2sin20sin70sin30sin50/cos10=1/4sin40sin50sin30/cos10=
=1/8sin80sin30/cos10=1/8cos10sin30/cos10=
=1/8sin30=1/8*1/2=1/16=0.0625

или

sin10sin30sin50sin70=1/2sin10sin50sin70=
=1/4(cos40-cos60 )sin70=1/4(cos40-0.5)sin70=
=1/4cos40sin70-1/8sin70=1/8(sin110+sin30)-1/8sin70=
=1/8sin110+1/16-1/8sin70=1/8sin(180-70)+1/16-1/8sin70=
=1/8sin70+1/16-1/8sin70=1/16=0.0625

Answer 2

sin10sin30sin50sin70=1/2[(cos60°-cos80°)]1/2[(cos20°-cos80°)]=1/4(0.5-0.17)(0.93-0.17)≈0.0625