General solution

Question

Cos^2 +3sin= -3

Answer 1

cos^2 x + 3sinx = -3
1 - sin^2 x + 3sinx + 3 = 0
sin^2 x - 3sinx - 4 = 0
(sinx -4)(sinx + 1) = 0
sinx = 4 , which is not possible
or
sinx = -1
x = 3π/2
since the period of sinx is 2π

general solution:
x = 3π/2 + 2kπ, where k is an integer.