15 -1 пример доказать, что sin10°sin30°sin50°sin70°=1/16 - вопрос №842215015110305070116 от lera556556 04.01.2022 14:00

Question

Алгебра: 15 -1 пример доказать, что sin10°sin30°sin50°sin70°=1/16

lera556556 · Answer

Sin10sin30sin50sin70=cos10sin10sin30sin50sin70/cos10==1/2sin20sin70sin30sin50/cos10=1/4sin40sin50sin30/cos10==1/8sin80sin30/cos10=1/8cos10sin30/cos10==1/8sin30=1/8*1/2=1/16=0.0625илиsin10sin30sin50sin70=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...