Question

5arctg(-√3)-3arccos(-√2/2)
2arcctg1+3arcsin(-1/2)

Answer 1

$5arctg(- \sqrt{3} )-3arccos(- \frac{ \sqrt{2} }{2} ) = \\ = 5 \times ( - \frac{\pi}{3}) - 3 \times \frac{3\pi}{4} = \\ = - \frac{5\pi}{3} - \frac{9\pi}{4} = \frac{ - 20\pi - 27\pi}{12} = \\ = - \frac{47\pi}{12} = - 3 \frac{11}{12} \pi$
$2arcctg1+3arcsin(- \frac{1}{2} ) = \\ = 2 \times \frac{\pi}{4} + 3 \times ( - \frac{ \pi }{6} ) = \\ = \frac{\pi}{2} - \frac{\pi}{2} = 0$