What is the general solution for sqrt(2)=cos(x)+sin(x) ?

The general solution for sqrt(2)=cos(x)+sin(x) is x=2pin+pi/4

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sqrt(2)=cos(x)+sin(x)

2 = cos (x) + sin (x)

x = 2 πn + \frac{π}{4}

Solution steps

2 = cos (x) + sin (x)

Switch sides

cos (x) + sin (x) = 2

Rewrite using trig identities

2 sin (x + \frac{π}{4}) = 2

Divide both sides by

2

sin (x + \frac{π}{4}) = 1

General solutions for

sin (x + \frac{π}{4}) = 1

x + \frac{π}{4} = \frac{π}{2} + 2 πn

Solve

x + \frac{π}{4} = \frac{π}{2} + 2 πn : x = 2 πn + \frac{π}{4}

x = 2 πn + \frac{π}{4}

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

cos (2 x) - 5 cos (x) - 1 = 0

3 + 3 cos (θ) = 3

csc^{2} (x) = 3 csc (x) + 4

4 cot (2 θ) = 0

What is the general solution for sqrt(2)=cos(x)+sin(x) ?
The general solution for sqrt(2)=cos(x)+sin(x) is x=2pin+pi/4