Tg x - tg (7π/2 - x) = 1

Question

Tg x - tg (7π/2 - x) = 1

Answer 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