6 син ^2х -5 кос х +5=0

6sin^2 x-5cos x +5=0

6(1-cos^2 x)- 5cos x +5=0

6 - 6cos^2 x- 5cos x +5=0 / :(-1)

6cos^2 x +5cos x-11=0

Cos x =t ; -1<=x<=1

6t^2+5t-11=0

D= 25+ 11×4×6=25+264= 289

T1=(-5+17)/12=1

T2=(-5-12)/12<-1

Sin x = 1

X= pi/2 + 2pi n