What is the solution set of 2 cos2 plus sinx -1 equals 0?

OK. Let's give it a whirl:

2 cos2 + sin - 1 = 0

Remember that cos2 = 1 - sin2 . Then, substitute that in the given equation

to see whether there appears to be any chance that it makes life easier:

2 (1 - sin2) + sin - 1 = 0

Eliminate parentheses :

2 - 2 sin2 + sin - 1 = 0

Combine like terms, clean it up, and multiply each side by -1 :

2 sin2 - sin - 1 = 0

This looks factorable:

(2 sin + 1) (sin - 1) = 0

Now we have it within our grasp.

2 sin(x) = 0

sin(x) = 0

x = + or - N pi

sin(x) - 1 = 0

sin(x) = 1

x = pi/2 + 2N pi

'x' is 90 degrees, and every multiple of 180 degrees.