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

danilmuratov20p02c8m danilmuratov20p02c8m    3   14.09.2019 03:10    1

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natashalixarev natashalixarev  07.10.2020 13:16
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
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