Determine the general solution of cos2x -4sinx+5=0

Question

Can't recall what the general solution is

Answer 1

This equation will have multiple roots and you need to determine an expression for all of those roots.

First, I would suggest you graph the equation and you will see what the solutions are.

The write cos 2x as 1 - 2 sin² x and substitute

1 - 2 sin² x - 4 sin x + 5 = 0 => sin² x + 2 sin x - 3 = 0

The roots of this equation are sin x = 1 and sin x = -3.

The negative root is impossible, but sin x = 1 whenever x = π/2 + 2πk where k is an integer.  That should match your graph!