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

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

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

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

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

Solution steps

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

Subtract

1

from both sides

sin^{2} (x) - cos (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 = π + 2 πn

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

Combine all the solutions

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

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

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

cos (x) = 9

sec (θ) = \frac{3}{5}

cos (3 x) + 2 cos (x) = 0

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