Question

Обчисліть вираз
sin 11П/30×cos п/5-cos 11п/30×sin П/5​

Answer 1

Ответ:

$\displaystyle \frac{1}{2}$

Пошаговое объяснение:

формула

$\displaystyle \begin{array}{|c|}\cline{1-} sin(\alpha-\beta)=sin\alpha cos\beta-cos\alpha sin\beta\\ \cline{1-}\end{array}$

$\displaystyle sin\frac{11\pi}{30}cos\frac{\pi}{5}-cos\frac{11\pi}{3}sin\frac{\pi}{5}=\\\\\\sin \left(\frac{11\pi}{30}-\frac{\pi}{5}= \right) =sin \left(\frac{11\pi}{30}-\frac{6\pi}{30}\right)=sin \frac{5\pi}{30}=sin \frac{\pi}{6}=\frac{1}{2}$