Question

11. (97-10-54) Упростите выражение​

Answer 1

$\displaystyle\bf\\\frac{Cos18^\circ\cdot Cos28^\circ+Cos108^\circ\cdot Sin208^\circ }{Sin18^\circ\cdot Sin78^\circ+Sin108^\circ\cdot Sin168^\circ}=\\\\\\=\frac{Cos18^\circ\cdot Cos28^\circ+Cos(90^\circ+1 8^\circ)\cdot Sin(180^\circ+28^\circ) }{Sin18^\circ\cdot Sin78^\circ+Sin(90^\circ+18^\circ) \cdot Sin(90^\circ+78^\circ) }=$

$\displaystyle\bf\\=\frac{Cos18^\circ\cdot Cos28^\circ+Sin18^\circ\cdot Sin28^\circ }{Sin18^\circ\cdot Sin78^\circ+Cos18^\circ\cdot Cos78^\circ}=\frac{Cos(18^\circ-28^\circ) }{Cos(18^\circ-78^\circ)} =\\\\\\=\frac{Cos10^\circ}{Cos60^\circ }=\frac{Cos10^\circ }{\frac{1}{2} } =2Cos10^\circ$