Question

ctg²(x-π/2)-ctg(x-3π/2)-2=0

Answer 1

${ctg}^{2} (x - \binom{\pi}{2} ) - ctg(x - \frac{3\pi}{2} ) - 2 = 0 \\ {tg}^{2} x - tg \: x - 2 = 0 \\ tg \: x = y$
${y}^{2} - y - 2 = 0 \\ y = - 1 \\ y = 2$
$tg \: x = - 1 \\ x = \pi \times n - \frac{\pi}{4} \\ tg \: x = 2\\ x = \pi \times n + ctg \: 2$