This equation appears to be an identity. Let’s check it out.
9sec²(x)-5tan²(x)=5+4sec²(x),
(9-4)sec²(x)=5+5tan²(x),
5sec²(x)=5+5tan²(x),
sec²(x)=1+tan²(x), by dividing through by 5,
1=cos²(x)+sin²(x), by multiplying through by cos²(x).
This is an identity (true for all x), so the original equation was an identity.