tg 1⁰ * tg 2⁰ * tg 3⁰ * * tg 89⁰=
= tg 1⁰ * tg 2⁰ * tg 3⁰ * ...tg 44⁰*tg45⁰*tg46⁰.. * tg 89⁰=
=tg 1⁰ * tg 2⁰ * tg 3⁰ * ...tg 44⁰*tg45⁰*ctg44⁰.. * ctg 1⁰=
=(tg 1⁰* ctg 1⁰)*(tg 2⁰* ctg 2⁰)*...*(tg 44⁰* ctg 44⁰)*tg45⁰=
=1*1*..*1*1=1
ответ: 1
так как tg(90⁰-x)=ctg x
tg x * ctg x=1
tg1*tg2*tg88*tg89=(tg1*tg89)*(tg2*tg88)*(tg44*tg46)*tg45=
=(cos(88-cos90)/(cos88+cos90))*(cos(86-cos90)/(cos86+cos90))*...((cos(2-cos90)/(cos2+cos90))*tg45=
=cos88/cos88 + cos86/cos86**cos2/cos2 *tg45=1
tg 1⁰ * tg 2⁰ * tg 3⁰ * * tg 89⁰=
= tg 1⁰ * tg 2⁰ * tg 3⁰ * ...tg 44⁰*tg45⁰*tg46⁰.. * tg 89⁰=
=tg 1⁰ * tg 2⁰ * tg 3⁰ * ...tg 44⁰*tg45⁰*ctg44⁰.. * ctg 1⁰=
=(tg 1⁰* ctg 1⁰)*(tg 2⁰* ctg 2⁰)*...*(tg 44⁰* ctg 44⁰)*tg45⁰=
=1*1*..*1*1=1
ответ: 1
так как tg(90⁰-x)=ctg x
tg x * ctg x=1
tg1*tg2*tg88*tg89=(tg1*tg89)*(tg2*tg88)*(tg44*tg46)*tg45=
=(cos(88-cos90)/(cos88+cos90))*(cos(86-cos90)/(cos86+cos90))*...((cos(2-cos90)/(cos2+cos90))*tg45=
=cos88/cos88 + cos86/cos86**cos2/cos2 *tg45=1