Tg x - tg (7π/2 - x) = 1

Tgx-tg (7π/2-x) = 1

tgx-ctgx=1

tgx-1/tgx=1

tg²x-tgx-1=0, tgx≠0

tgx=a

a²-a-1=0

D=1+4=5

a1 = (1-√5) / 2⇒tgx = (1-√5) / 2⇒x=arctg (1-√5) / 2+πn, n∈z

a2 = (1+√5) / 2⇒tgx = (1+√5) / 2⇒x=arctg (1+√5) / 2+πn, n∈z