Question

Найдите значение выражения 5sin 13pi/12*cos 13pi/12

Answer 1

$5sin(\frac{13\pi}{12})cos(\frac{13\pi}{12}) = \frac{5}{2}\cdot2sin(\frac{13\pi}{12})cos(\frac{13\pi}{12}) = \frac{5}{2}sin(2\cdot\frac{13\pi}{12})=\frac{5}{2}sin(\frac{13\pi}{6})=\frac{5}{2}sin(2\pi+\frac{\pi}{6})$$=\frac{5}{2}sin(\frac{\pi}{6})=\frac{5}{2}\cdot\frac{1}{2}=\frac{5}{4}$