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/2+2pin,x=(3pi)/2+2pin,x=2pin

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

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

x = \frac{π}{2} + 2 πn, x = \frac{3 π}{2} + 2 πn, x = 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) = 0, cos (x) = 1

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

cos (x) = 1 : x = 2 πn

Combine all the solutions

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

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

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

2 cos (x) + sin (2 x) = 0, 0 \leq x \leq 2 π

tan^{2} (x) sin (x) = sin (x)

2 sin (2 x) - 3 = 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/2+2pin,x=(3pi)/2+2pin,x=2pin