Вычисления и преобразования

$$\sin (\alpha - 7\pi) = \sin (\alpha - \pi - 6\pi) = \sin (\alpha - \pi) = -\sin \alpha$$ $$\cos \left(\frac{3\pi}{2} + \alpha\right) = \sin \alpha, \quad \sin (\alpha + \pi) = -\sin \alpha$$ $$\frac{2(-\sin \alpha) + \sin \alpha}{-\sin \alpha} = \frac{-\sin \alpha}{-\sin \alpha} = 1$$

$$\tg(5\pi - \gamma) = \tg(\pi - \gamma) = -\tg \gamma, \quad \tg(-\gamma) = -\tg \gamma$$ $$5(-\tg \gamma) - (-\tg \gamma) = -5\tg \gamma + \tg \gamma = -4\tg \gamma = -4 \cdot 7 = -28$$

$$\sin\left(\frac{7\pi}{2} - \alpha\right) = \sin\left(3\pi + \frac{\pi}{2} - \alpha\right) = -\cos \alpha$$ $$\cos \alpha = -\sqrt{1 - \sin^2 \alpha} = -\sqrt{1 - 0,64} = -0,6 \quad (\text{II четверть})$$ $$-\cos \alpha = 0,6$$

$$\cos\left(\frac{3\pi}{2} + \alpha\right) = \sin \alpha$$ $$\sin \alpha = -\sqrt{1 - \cos^2 \alpha} = -\sqrt{1 - \frac{144}{169}} = -\frac{5}{13} \quad (\text{IV четверть})$$ $$26 \sin \alpha = 26 \cdot \left(-\frac{5}{13}\right) = -10$$

$$\tg\left(\alpha + \frac{5\pi}{2}\right) = \tg\left(\alpha + \frac{\pi}{2}\right) = -\ctg \alpha = -\frac{1}{\tg \alpha} = -\frac{1}{0,4} = -\frac{1}{\frac{2}{5}} = -\frac{5}{2}=-2,5$$