Question

3 +9 cosx = 5sin^2x

Answer 1

3+9cosx=5(1-cos²x)
3+9cosx=5-5cos²x
5cos²x+9cosx-2=0
cosx=a, |a|≤1
5a²+9a-2=0
D=81-4*5*(-2)=81+40=121
a1=(-9-11)/10=-2<-1
a2=(-9+11)/10=0,2
cosx=0,2
x=arccjo0,2+2πn, n∈Z