Знайти tgx, якщо ctg(x-π/4)=4/3

Question

Знайти tgx, якщо ctg(x-π/4)=4/3

Answer 1

Ctg(x - π/4) = 4/3,   tgx - ?
tg(x - π/4) = 3/4
(tgx - tgπ/4)/(1 + tgx*tgπ/4) = 3/4
(tgx - 1)/(1 + tgx) = 3/4
4(tgx - 1) = 3(1 + tgx)
4tgx -4 = 3 + 3tgx 
tgx = 7