1.sin12+sin24+sin36+sin48+sin60 2.cos20+cos40+sin10+cos80+cos100 - вопрос №865508211224364860220401080100 от ник3123 09.10.2020 08:23

Question

Алгебра: 1.sin12+sin24+sin36+sin48+sin60 2.cos20+cos40+sin10+cos80+cos100

ник3123 · Answer

1.sin12+sin24+sin36+sin48+sin60=2sin30cos18+2sin30cos6+sin60=
=cos18+cos6+√3/2=2cos12cos6+√3/2
2.cos20+cos40+sin10+cos80+cos100=2cos60cos40+2cos60cos20+sin10=
=cos40+cos20+sin10=2cos30cos10+sin10=√3cos10+sin10=
=2(√3/2cos10+1/2sin10)=2sin(10+60)=2sin70