Question

tgx+3ctgx=0 . tgx-4ctgx=0

Answer 1

$tgx+3ctgx=0\tgx+frac{3}{tgx}=0|*tgx\tg^2x+3=0\tg^2x=-3\xinvarnothing\\tgx-4ctgx=0\tgx-frac{4}{tgx}=0|*tgx\tg^2x-4=0\tg^2x=4\tgx=2 tgx=-2\x=arctg2+pi n;x=-arctg2+pi n;nin Z$