Tgx-tg(7p:2-x)=1 P-число пи

Question

Tgx-tg(7p:2-x)=1
P-число пи

Answer 1

Tgx-ctgx=1
tgx-1/tgx=1
tg²x-tgx-1=0
tgx=a
a²-a-1=0
D=1+4=5
a1=(1-√5)/2⇒tgx=(1-√5)/2⇒x=arctg(1-√5)+πn
a2=(1+√5)/2⇒tgx=(1+√5)/2⇒x=arctg(1+√5)+πn