Question

Упростите выражение
Даю 25 баллов

Answer 1

$tg1^{o}*tg2^{o}*tg3^{o}*...tg87^{o}*tg88^{o}*tg89^{o}=tg1^{o}*tg2^{o}*tg3^{o}*...*tg45^{o}*...*tg(90^{o}-3^{o})*tg(90^{o}-2^{o})*tg(90^{o}-1^{o})=tg1^{o}*tg2^{o}*tg3^{o}*...*tg45^{o}*...*Ctg3^{o}*Ctg2^{o} *Ctg1^{o}=(tg1^{o}*Ctg1^{o})(tg2^{o}*Ctg2^{o})(tg3^{0}*Ctg3^{o})*...*tg45^{o}*...(tg44^{o}*Ctg44^{o} )=1*1*1*...*1*...*1=1$

Answer 2

tg1*tg2*tg3.....tg87*tg88*tg89=(tg1*tg89)*

(tg2*tg88)......(tg45*tg45)=(tg1*ctg1)(tg2*tg2)

........tg45*ctg45=1