12. Вычислите: a) arcsin; B) arctg (-1); д) arcos 0; *) cos (arccos + arcsin)

Ответ: a) π/6; б) -π/4; д) π/2; ж) 1

a) arcsin(1/2)\[\arcsin\left(\frac{1}{2}\right) = \frac{\pi}{6}\]

б) arctg(-1)\[\arctan(-1) = -\frac{\pi}{4}\]

д) arccos(0)\[\arccos(0) = \frac{\pi}{2}\]

ж) cos(arccos(√2/2) + arcsin(√2/2))\[\cos\left(\arccos\left(\frac{\sqrt{2}}{2}\right) + \arcsin\left(\frac{\sqrt{2}}{2}\right)\right) = \cos\left(\frac{\pi}{4} + \frac{\pi}{4}\right) = \cos\left(\frac{\pi}{2}\right) = 0\]

Ответ: a) π/6; б) -π/4; д) π/2; ж) 0