Question

tg(x+pi/4) + 2tg(x-pi/4)=1

Answer 1

(tgx+1)/(1-tgx) +2(tgx-1)/(tgx+1)=1
-(tgx+1)/(tgx-1) +2(tgx-1)/(tgx+1)=1
-tg²x-2tgx-1+2tg²x-4tgx+2=tg²x-1          tgx≠1 U tgx≠-1
tg²x-6tgx+1-tg²x+1=0
6tgx=2
tgx=1/3⇒x=arctg1/3+πn