решите уравнение: 7sin^2x+4sinxcosx - 3cos^2x=0

Question

решите уравнение:

7sin^2x+4sinxcosx - 3cos^2x=0

Answer 1

7sin^2x+4sinxcosx - 3cos^2x=0   /: cos^2x≠0
7tg^2x + 4tgx - 3 = 0
Пусть tgx=t, t ∈( - беск; + беск.)
7t^2 + 4t - 3 = 0
t1 =  - 1
t2 =  3/7

1) tgx = - 1  ==> x = - pi/4 + pik, k c Z
2) tgx = 3/7 ==> x = arctg(3/7) + pik, k c Z