Question

Вычислите

frac { frac {cos55^{circ}} {sin55^{circ}} * sin110^{circ} - 1 } { cos110^{circ} }
плиз хелп

Answer 1

$frac { frac {cos55^{circ}} {sin55^{circ}} * sin110^{circ} - 1 } { cos110^{circ} } =frac{ctg55^{circ}*sin110^{circ}-1}{cos110^{circ}}=\\ =frac{2sin55^{circ}cos55^{circ}ctg55^{circ}-1}{cos110^{circ}}= frac{2cos^{2}55^{circ}-1}{cos110^{circ}}=\\=frac{2cos^{2}55^{circ}-cos^{2}55^{circ}-sin^{2}55^{circ}}{cos110^{circ}}=\\ =frac{cos55^{2}^{circ}-sin55^{2}^{circ}}{cos110^{circ}}=frac{cos110^{circ}}{cos110^{circ}}=1$