Question

решите уравнения.5sin2х+6cosx-6=0

Answer 1

$5sin ^{2} x+6cosx-6=0$
ОДЗ:х∈R
$5*(1-cos ^{2} x)-6cosx-6=0$
$5-5cos ^{2} x-6cosx-6=0$
$-5cos ^{2} x-6cosx-1=0$
cosx=t
-5t²-6t-1=0
D=16>0(2рдк)
t1= -1
t2= -1/5
cosx= -1     или      cosx= -1/5
x= П+2Пn; n∈Z      x= П-arccos1/5+2Пn;n ∈Z