Question

tg^2x+ctg^2x=tgx+ctgx

Answer 1

tg²x+2tgx*ctgx+ctg²x-2tgx*ctgx-(tgx+ctgx)=0
(tgx+ctgx)²-(tgx+ctgx)-2=0
tgx+ctgx=t
t²-t-2=0
t1=-1   t2=2
tgx+1/tgx=-1
tg²x+tgx+1/tgx=0
Кoрней нет,т.к. Д<0

tgx+1/tgx=2
tg²x-2tgx+1/tgx=0
(tgx-1)²/tgx=0
tgx=1
x=pi/4+pi*n