Условие задачи
Найдите значение выражения:
\(\displaystyle \frac{1}{2} + sin \frac{\pi}{12} \, sin \frac{5\pi}{12} - sin^2 \, \frac{\pi}{3}\)
Решение
\(\displaystyle \frac{1}{2} + sin \frac{\pi}{12} \, sin \frac{5\pi}{12} - sin^2 \frac{\pi}{3}= \frac{1}{2}-\frac{3}{4}+sin \frac{\pi}{12} \cdot sin (\frac{\pi}{2}-\frac{\pi}{12}) = \)
\(\displaystyle = \frac{1}{2} - \frac{3}{4}+sin \frac{\pi}{12}cos \frac{\pi}{12} = - \frac{1}{4}+\frac{1}{2}sin \frac{\pi}{6} = - \frac{1}{4}+\frac{1}{4}=0. \)
Ответ
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