第13章 13.10

(1)

$\sin x - 1 = 0 \qquad \sin x = 1 \qquad x = \frac{\pi}{2}, \frac{5}{2}\pi, \cdots \qquad x = \frac{\pi}{2} + 2n\pi$

(2)

$2\sin x + 1 = 0 \qquad \sin x = -\frac{1}{2} \qquad x = \frac{7}{6}\pi + 2n\pi, -\frac{\pi}{6} + 2n\pi$

(3)

$\tan x + 1 = 0 \qquad \tan x = -1 \qquad x = \frac{3\pi}{4} + n\pi$

(4)

$\cos x - 2\cos^2 x = 0 \qquad \cos x(1 - 2\cos x) = 0 \qquad \cos x = 0, \frac{1}{2} \qquad x = \frac{\pi}{2} + n\pi, \pm\frac{\pi}{3} + 2n\pi$

(5)

$2\sin^2 x + \sin x - 1 = 0 \qquad (2\sin x - 1)(\sin x + 1) = 0 \qquad \sin x = \frac{1}{2}, -1$

$x = \frac{\pi}{6} + 2n\pi, \frac{5}{6}\pi + 2n\pi, \frac{3}{2}\pi + 2n\pi$

(6)

$\cos^2 x - 3\cos x + 2 = 0 \qquad (\cos x - 2)(\cos x - 1) = 0 \qquad \cos x = 1 \qquad x = 2n\pi$

(7)

$\sin 2x + \sin x = 0 \qquad 2\sin x \cos x + \sin x = 0 \qquad \sin x(2\cos x + 1) = 0 \qquad \sin x = 0 \qquad \cos x = -\frac{1}{2}$

$(2n+1)\pi, \frac{2}{3}\pi + 2n\pi, \frac{4}{3}\pi + 2n\pi$

(8)

$\cos 2x + \sin^2 x = 0 \qquad \cos^2 x - \sin^2 x + \sin^2 x = 0 \qquad \cos^2 x = 0 \qquad x = \frac{\pi}{2} + n\pi$