Question

cos^2x + sinx + 1 = 0
(1-sin^2x) + (sinx+1) = 0
(1-sinx) (1+sinx) + (sinx +1) = 0
(1 + sinx) (1-sinx +1) = 0
Dont understand how this last step was made ???

Answer 1

well you are almost there....

the 2nd factor can be simplified

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

so then in factored form your equation is

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

so you need to solve

1 + sin(x) = 0

and

2 - sin(x) = 0 doesn't exist as sin(x)< 1

Answer 2

so all you need to do is solve

1 + sin(x) = 0

or

sin(x) = -1

that should be easy to calculate.