Question

arctgx+arctg(-2)=arcctg(-2)

Answer 1

$arctg(x)+arctg(-2)=arcctg(-2)\\arctg(x)=arctg(2)-arcctg(2)\\x=tg(arctg(2)-arcctg(2))\\x=\frac{tg(-arcctg(2))+tg(arctg(2))}{1-tg(-arcctg(2))tg(arctg(2))}\\x=\frac{2-\frac{1}{2}}{1+1}=\frac{3}{4}$