3 sin²x+10sin x cos x+3cos² x =0​

Question

3 sin²x+10sin x cos x+3cos² x =0​

Answer 1

3 sin²x+10sin x cos x+3cos² x =0 | : cos² x

3tg² x+10tg x+3=0

D=100-36=64

tg x= (-10+8)/6= -1/3   tg x= -1/3  x= - arctg(1/3)+πn  n∈Z

tg x=(-10-8)/6 = -3       tg x= -3    x=  - arctg (3)+πn    n∈Z