Question

На помоооощь!!! Срочно!!!

Answer 1

Ответ 1
=(sin40+sin160)(sin20+sin140)+
+(sin130-sin110)(sin50-sin70)=
=(sin40+sin(180-20))(sin20+sin(180-40))+
+(sin(180-50)-sin(180-70))*(sin50-sin70)=
=(sin40+sin20)(sin20+sin40)+
+(sin50-sin70)(sin50-sin70)=
=(sin40+sin20)^2+(sin(90-40)-sin(90-20))^2=
=(sin40+sin20)^2+(cos40-cos20)^2=
=sin^2(40)+cos^2(40)+sin^2(20)+cos^2(2)+2sin40sin20-2cos40cos20=
=2-2(-sin40sin20+cos40cos20)=2-2cos60=2-2*1/2=2-1=1