Tgxtg10°+tg10°tg50°+tg50°tgx=1

Question

Tgxtg10°+tg10°tg50°+tg50°tgx=1

Answer 1

Tgxsin60/cos10cos50+sin10sin50/cos10cos50=1
√3/2tgx+1/2(cos40-cos60)=cos10cos50
√3/2tgx+1/2cos40-1/4=10cos40+1/4
√3/2tgx=1/2
tgx=√3/3
x=arctg√3/3+πk k∈Z