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

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

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

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

x = \frac{π}{2} + 2 πn

Solution steps

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

Subtract

- 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{π}{2} + 2 πn

Combine all the solutions

x = \frac{π}{2} + 2 πn

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

cos^{2} (x) + 3 cos (x) = 1

cot^{2} (x) = \frac{tan ( x )}{2}

tan (θ) = \frac{3.2}{4.1}

5 sec (x) tan (x) = 0

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