Question

Вычислите:

1) arctg √3 - arctg1 + arcctg (-√3)

2) tg (arcctg √3/3)

3) arcctg (sin π/2)

Answer 1

$arctan(sqrt3)-arctan (1)+arcctg(-sqrt3)= frac{pi}{3}- frac{ pi }{4}+ frac{5 pi }{6}= frac{4 pi-3pi+10pi}{12}=\\= frac{11 pi }{12} \\\ tan (arctan( frac{sqrt3}{3})=tan( frac{pi}{6})= frac{sqrt 3}{3}\\\ arcctg(sin frac{pi}{2})=arcctg(1)= frac{pi}{4}$