Question

sin²x +14sinxcosx = 15cos²x

Answer 1

sin²x+14sinxcosx=15cos²x
sin²x+14sinxcosx-15cos²x=0 |: cos²x
tg²x+14tgx-15=0
Обозначим:  tgx= t тогда
t²+14t-15=0
D= 196+60 = 256
t₁= -14+16/2 = 1
t₂= -14-16/2 = -15


1)tgx= 1
x= π/4+πn, n∈z

2)tgx= -15
x= arctg(-15)+πn
x= -arctg15+πn,n∈z