Question

найти значение выражения

Answer 1

$\frac{\sin{(\alpha+\beta)-2\cdot \cos{\alpha}\cdot \sin{\beta}}}{2\sin{\alpha}\cdot\sin{\beta}+\cos{(\alpha+\beta)}} =\frac{\sin{\alpha}\cos{\beta+\cos{\alpha}\cdot \sin{\beta}-2\cdot \cos{\alpha}\cdot\sin{\beta}}}{2\sin{\alpha}\cdot\sin{\beta}+\cos{\alpha}\cdot\cos{\beta}-\sin{\alpha}\cdot\sin{\beta}}=\frac{\sin{\alpha}\cos{\beta-\cos{\alpha}\cdot \sin{\beta}}}{\sin{\alpha}\cdot\sin{\beta}+\cos{\alpha}\cdot\cos{\beta}}= \\ \\ =\frac{\sin{(\alpha-\beta)}}{\cos{(\alpha-\beta)}}=\frac{\sin135^o}{\cos135^o}=$

$=tg \, 135^o= tg \, (90^0+45^o)= - ctg \, 45^o= -1$