(tgx+ctgx)^2 - (tgx-ctgx)^2 = 0

(tgx+ctgx)((tgx+ctgx) - (tgx-ctgx)) = 0
(tgx+ctgx)(tgx+ctgx - tgx + ctgx) = 0
(tgx+ctgx)(2ctgx) = 0
2ctgx(tgx+ctgx) = 0

Уравнение упрощено до 2ctgx(tgx+ctgx) = 0.