3tg^2x+ctg^2x=4?????????

Question

3tg^2x+ctg^2x=4?????????

Answer 1

3tg²x+1/tg²x=4 tg²x=y;3y+1/y-4=0 3y²-4y+1=0;y₁=1;y₂=⅓ 1) tg²x=1;tgx=±1;x=±π/4+πn,n∈Z 2) tg²x=⅓;tgx=±1/√3;x=±π/6+πk,k∈Z.