Tg 20 +tg 25 +ctg70 ctg 245

Решите задачу:

$tg20+tg25+ctg70*ctg245=$ $tg20+tg25+ctg(90-20)*ctg(270-25)=tg20+tg25+tg20*tg25=$

$=\frac{sin20}{cos20}+ \frac{sin25}{cos25}+ \frac{sin20*sin25}{cos20*cos25}=$ $\frac{sin20*cos25+sin25*cos20+sin20*sin25}{cos20*cos25}=$

$=\frac{0.5*(-sin5+sin45)+0.5*(sin5+sin45)+0.5*(cos5-cos45)}{0.5*(cos5+cos45)}=$

$=\frac{-0.5*sin5+0.5sin45+0.5*sin5+0.5*sin45+0.5*cos5-0.5*cos45}{0.5*(cos5+cos45)}=$

$=\frac{sin45+0.5*cos5-0.5*cos45}{0.5*(cos5+cos45)}= \frac{\frac{\sqrt{2}}{2}+0.5*cos5-\frac{\sqrt{2}}{4}}{0.5*(cos5+cos45)}=\frac{\frac{\sqrt{2}}{4}+0.5*cos5}{0.5*(cos5+\frac{\sqrt{2}}{2})}=$ $=\frac{0.5*(\frac{\sqrt{2}}{2}+cos5)}{0.5*(cos5+\frac{\sqrt{2}}{2})}=1$