1)
![(1+tg^{2}a)(1+ctg^{2}a)*tg^{2}a-(1-tg^{2}a)^{2}=(1+tg^{2}a)(1+ \frac{1}{tg^{2}a})*tg^{2}a-(1-2tg^{2}a+tg^{4}a)=(1+tg^{2}a)(tg^{2}a+1)-1+2tg^{2}a-tg^{4}a=(1+tg^{2}a)^{2}-1+2tg^{2}a-tg^{4}a=1+2tg^{2}a+tg^{4}a-1+2tg^{2}a-tg^{4}a=4tg^{2}a](https://tex.z-dn.net/?f=%281%2Btg%5E%7B2%7Da%29%281%2Bctg%5E%7B2%7Da%29%2Atg%5E%7B2%7Da-%281-tg%5E%7B2%7Da%29%5E%7B2%7D%3D%281%2Btg%5E%7B2%7Da%29%281%2B+%5Cfrac%7B1%7D%7Btg%5E%7B2%7Da%7D%29%2Atg%5E%7B2%7Da-%281-2tg%5E%7B2%7Da%2Btg%5E%7B4%7Da%29%3D%281%2Btg%5E%7B2%7Da%29%28tg%5E%7B2%7Da%2B1%29-1%2B2tg%5E%7B2%7Da-tg%5E%7B4%7Da%3D%281%2Btg%5E%7B2%7Da%29%5E%7B2%7D-1%2B2tg%5E%7B2%7Da-tg%5E%7B4%7Da%3D1%2B2tg%5E%7B2%7Da%2Btg%5E%7B4%7Da-1%2B2tg%5E%7B2%7Da-tg%5E%7B4%7Da%3D4tg%5E%7B2%7Da)
- что и требовалось доказать
2)
![(1+sin^{2}b)*ctg^{2}b- \frac{1}{sin^{2}b}=(1+sin^{2}b)*\frac{cos^{2}b}{sin^{2}b}- \frac{1}{sin^{2}b}=\frac{cos^{2}b}{sin^{2}b}+cos^{2}b- \frac{1}{sin^{2}b}=\frac{cos^{2}b-1}{sin^{2}b}+cos^{2}b=\frac{-(1-cos^{2}b)}{sin^{2}b}=\frac{-sin^{2}b}{sin^{2}b}=-1](https://tex.z-dn.net/?f=%281%2Bsin%5E%7B2%7Db%29%2Actg%5E%7B2%7Db-+%5Cfrac%7B1%7D%7Bsin%5E%7B2%7Db%7D%3D%281%2Bsin%5E%7B2%7Db%29%2A%5Cfrac%7Bcos%5E%7B2%7Db%7D%7Bsin%5E%7B2%7Db%7D-+%5Cfrac%7B1%7D%7Bsin%5E%7B2%7Db%7D%3D%5Cfrac%7Bcos%5E%7B2%7Db%7D%7Bsin%5E%7B2%7Db%7D%2Bcos%5E%7B2%7Db-+%5Cfrac%7B1%7D%7Bsin%5E%7B2%7Db%7D%3D%5Cfrac%7Bcos%5E%7B2%7Db-1%7D%7Bsin%5E%7B2%7Db%7D%2Bcos%5E%7B2%7Db%3D%5Cfrac%7B-%281-cos%5E%7B2%7Db%29%7D%7Bsin%5E%7B2%7Db%7D%3D%5Cfrac%7B-sin%5E%7B2%7Db%7D%7Bsin%5E%7B2%7Db%7D%3D-1)
7√1,7=√83,3
1,2√20=√28,8
√83,3>√28,8⇒7√1,7>1,2√20
40*2=80% прошёл турист за 2 дня
100-80 = 20% осталось на 3 день
20%=15км
15:2=7,5 - 10%
7,5*10=75 км путь туриста
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Надеюсь, что ты успеешь переписать)