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

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

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sqrt(1-sin(x))=cos(x)

1 - sin (x) = cos (x)

x = \frac{π}{2} + 2 πn, x = 2 πn

Solution steps

1 - sin (x) = cos (x)

Square both sides

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

Subtract

cos^{2} (x)

from both sides

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

Rewrite using trig identities

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

Solve by substitution

sin (x) = 1, sin (x) = 0

sin (x) = 1 : x = \frac{π}{2} + 2 πn

sin (x) = 0 : x = 2 πn, x = π + 2 πn

Combine all the solutions

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

Verify solutions by plugging them into the original equation

x = \frac{π}{2} + 2 πn, x = 2 πn

sec^{2} (x) = sec (x) + 2

(cot (θ) - 3) (2 sin (θ) + 1) = 0

5 sin (θ) - 4 = 0

x, cos (x) + cos (x + y) = 0

cosh (x) = 1

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