Question

упростите пожалуйста как можно скорее

Answer 1

$Ctg245^{0}Ctg205^{0} (Sin265^{0}Cos175^{0}+Sin5^{0}Cos95^{0})=\\\\=Ctg(270^{0}-25^{0})*Ctg(180^{0}+25^{0})*[Sin(270^{0}-5^{0})*Cos(180^{0}-5^{0})+\\\\+Sin5^{0}*Cos(90^{0}+5^{0})]=\\\\=\underbrace{tg25^{0}*Ctg25^{0}}_{1} *[(-Cos5^{0})*(-Cos5^{0})+Sin5^{0}*(-Sin5^{0})]=\\\\=Cos^{2}5^{0}-Sin^{2}5^{0}=\boxed{Cos10^{0}}$

Answer 2

$ctg245^\circ \cdot ctg205^\circ \cdot (sin265^\circ \cdot cos175^\circ +sin5^\circ \cdot cos95^\circ )=\\\\\\=ctg(270^\circ -25^\circ )\cdot ctg(180^\circ +25^\circ )\cdot \Big(sin(270^\circ -5^\circ )\cdot cos(180^\circ -5^\circ )+\\\\+sin5^\circ \cdot cos(90^\circ +5^\circ )\Big)=\\\\\\=\underbrace {tg25^\circ \cdot ctg25^\circ }_{1}\cdot \Big(-cos5^\circ \cdot (-cos5^\circ )+sin5^\circ \cdot (-sin5^\circ )\Big)=\\\\\\=1\cdot (cos^25^\circ -sin^25^\circ )=cos10^\circ$