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

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

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

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

x = 2 πn, x = \frac{π}{2} + 2 πn, x = \frac{3 π}{2} + 2 πn

Solution steps

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

Subtract

sin^{2} (x) - 1

from both sides

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

Rewrite using trig identities

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

Solve by substitution

cos (x) = 1, cos (x) = 0

cos (x) = 1 : x = 2 πn

cos (x) = 0 : x = \frac{π}{2} + 2 πn, x = \frac{3 π}{2} + 2 πn

Combine all the solutions

x = 2 πn, x = \frac{π}{2} + 2 πn, x = \frac{3 π}{2} + 2 πn

csc (x) = \frac{5}{2}

csc (x) = \frac{5}{4}

3 cos (2 θ) = 9 cos (θ) - 6

4 sin (\frac{x}{3}) - 3 = 0

0 = sin (c)

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