Страница 161 номер 535, ГДЗ по алгебре за 10-11 класс Алимов - ответы и решение

1) \(\cos\left(\frac{\pi}{2} - x\right) = 1\)
\(\sin x = 1,\)
\(x = \dfrac{\pi}{2} + 2\pi k, k \in Z;\)

2) \(\sin\left(\frac{3\pi}{2} + x\right) = 1\)
\(-\cos x = 1,\)
\(\cos x = -1,\)
\(x = \pi + 2\pi k, k \in Z;\)

3) \(\cos(x - \pi) = 0\)
\(\cos(\pi - x) = 0,\)
\(-\cos x = 0,\)
\(x = \dfrac{\pi}{2} + \pi k, k \in Z;\)

4) \(\sin\left(x - \frac{\pi}{2}\right) = 1\)
\(-\sin\left(\dfrac{\pi}{2} - x\right) = 1,\)
\(-\cos x = 1,\)
\(\cos x = -1,\)
\(x = \pi + 2\pi k, k \in Z;\)

5) \(\sin(2x + 3\pi) \sin\left(3x + \frac{3\pi}{2}\right) - \sin 3x \cos 2x = -1\)
\(\sin 2x \cos 3x - \sin 3x \cos 2x = -1,\)
\(\sin(2x - 3x) = -1,\)
\(-\sin x = -1,\)
\(x = \dfrac{\pi}{2} + 2\pi k, k \in Z;\)

6) \(\sin\left(5x - \frac{3\pi}{2}\right) \cos(2x + 4\pi) - \sin(5x + \pi) \sin 2x = 0\)
\(\cos 5x \cos 2x + \sin 5x \sin 2x = 0,\)
\(\cos(5x - 2x) = 0,\)
\(3x = \dfrac{\pi}{2} + \pi k, k \in Z\)
\(x = \dfrac{\pi}{6} + \dfrac{\pi}{3}k, k \in Z.\)