Найдите значение выражения 8sin(−27π4)cos(31π4)\frac{8}{\sin\left(-\frac{27\pi}{4}\right)\cos\left(\frac{31\pi}{4}\right)}sin(−427π)cos(431π)8 Источник: Банк ФИПИ Показать решение Решение: sin(−27π4)=−sin(27π4)=−sin(6π+3π4)=−sin(3π4)=−22\sin\left(-\frac{27\pi}{4}\right) = -\sin\left(\frac{27\pi}{4}\right) = -\sin\left(6\pi + \frac{3\pi}{4}\right) = -\sin\left(\frac{3\pi}{4}\right) = -\frac{\sqrt{2}}{2}sin(−427π)=−sin(427π)=−sin(6π+43π)=−sin(43π)=−22 cos(31π4)=cos(8π−π4)=cos(−π4)=cos(π4)=22\cos\left(\frac{31\pi}{4}\right) = \cos\left(8\pi - \frac{\pi}{4}\right) = \cos\left(-\frac{\pi}{4}\right) = \cos\left(\frac{\pi}{4}\right) = \frac{\sqrt{2}}{2}cos(431π)=cos(8π−4π)=cos(−4π)=cos(4π)=22 8(−22)⋅(22)=8−24=8−12=−16\frac{8}{\left(-\frac{\sqrt{2}}{2}\right)\cdot\left(\frac{\sqrt{2}}{2}\right)} = \frac{8}{-\frac{2}{4}} = \frac{8}{-\frac{1}{2}} = -16(−22)⋅(22)8=−428=−218=−16 Ответ: -16