Страница 161 номер 533, ГДЗ по алгебре за 10-11 класс Алимов - ответы и решение
Доказать тождество (532—533). 1) \(\sin\left(\frac{7\pi}{6} + \alpha\right) = -\sin\left(\frac{\pi}{6} + \alpha\right)\); 2) \(\sin\left(\frac{5\pi}{4} + \alpha\right) = -\sin\left(\frac{3\pi}{4} - \alpha\right)\); 3) \(\cos\left(\alpha - \frac{2\pi}{3}\right) = -\cos\left(\frac{\pi}{3} + \alpha\right)\); 4) \(\cos\left(\alpha - \frac{2\pi}{3}\right) = \cos\left(\alpha + \frac{4\pi}{3}\right)\).
1) \(\sin\left(\frac{7\pi}{6} + \alpha\right) = -\sin\left(\frac{\pi}{6} + \alpha\right)\)
\(\sin\left(\dfrac{7\pi}{6} + \alpha\right) = \sin\left(\pi + \left(\dfrac{\pi}{6} + \alpha\right)\right) = -\sin\left(\dfrac{\pi}{6} + \alpha\right);\)
2) \(\sin\left(\frac{5\pi}{4} + \alpha\right) = -\sin\left(\frac{3\pi}{4} - \alpha\right)\)
\(\sin\left(\dfrac{5\pi}{4} + \alpha\right) = \sin\left(2\pi - \left(\dfrac{3\pi}{4} - \alpha\right)\right) = -\sin\left(\dfrac{3\pi}{4} - \alpha\right);\)
3) \(\cos\left(\alpha - \frac{2\pi}{3}\right) = -\cos\left(\frac{\pi}{3} + \alpha\right)\)
\(\cos\left(\alpha - \dfrac{2\pi}{3}\right) = \cos\left(\dfrac{2\pi}{3} - \alpha\right) =\)
\(= \cos\left(\pi - \left(\dfrac{\pi}{3} + \alpha\right)\right) = -\cos\left(\dfrac{\pi}{3} + \alpha\right);\)
4) \(\cos\left(\alpha - \frac{2\pi}{3}\right) = \cos\left(\alpha + \frac{4\pi}{3}\right)\)
\(\cos\left(\alpha - \dfrac{2\pi}{3}\right) = \cos\left(\dfrac{2\pi}{3} - \alpha\right) =\)
\(= \cos\left(2\pi - \left(\dfrac{4\pi}{3} + \alpha\right)\right) = \cos\left(\alpha + \dfrac{4\pi}{3}\right).\)
