Question

Вычислите

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

Answer 1

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