Sin^2x -2sinxcosx -3cos^2x=0

Question

Sin^2x -2sinxcosx -3cos^2x=0

Answer 1

Sin²x - 2sinxcosx - 3cos²x = 0
tg²x - 2tgx - 3 = 0
Пусть t = tgx.
t² - 2t - 3 = 0
t1 + t2 = 2
t1•t2 = -3
t1 = -1
t2 = 3
Обратная замена:
tgx = -1
x = -π/4 + πn, n ∈ Z
tgx = 3
x = arctg3 + πn, n ∈ Z.