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

cos (x) + 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

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

3 tan (\frac{1}{2} x) - 1 = 0

cos (x) = \frac{7}{11}

cos (x) = tan (x)

2 sin (x) = sin (x)

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