What is the general solution for -cos^2(x)=sin(x)+1 ?

The general solution for -cos^2(x)=sin(x)+1 is x=(3pi)/2+2pin

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

- cos^{2} (x) = sin (x) + 1

x = \frac{3 π}{2} + 2 πn

Solution steps

- cos^{2} (x) = sin (x) + 1

Subtract

sin (x) + 1

from both sides

- cos^{2} (x) - sin (x) - 1 = 0

Rewrite using trig identities

- 2 - sin (x) + sin^{2} (x) = 0

Solve by substitution

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

sin (x) = 2 :

No Solution

sin (x) = - 1 : x = \frac{3 π}{2} + 2 πn

Combine all the solutions

x = \frac{3 π}{2} + 2 πn

\frac{36}{sin ( 11 0 ^{\circ} )} = \frac{15}{sin ( x )}

6 sin (\frac{x}{2}) + 6 cos (x) = 0

cos (x) = 0.925

(sin (x) + 1) (2 sin^{2} (x) - 3 sin (x) - 2) = 0

\frac{sin ( A )}{9} = \frac{sin ( 10 8 ^{\circ} )}{6}

What is the general solution for -cos^2(x)=sin(x)+1 ?
The general solution for -cos^2(x)=sin(x)+1 is x=(3pi)/2+2pin