What is the general solution for solvefor x,sin(x)+cos(x)=1 ?

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

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solvefor x,sin(x)+cos(x)=1

solve for

x, sin (x) + cos (x) = 1

x = 2 πn, x = 2 πn + \frac{π}{2}

Solution steps

sin (x) + cos (x) = 1

Rewrite using trig identities

2 sin (x + \frac{π}{4}) = 1

Divide both sides by

2

sin (x + \frac{π}{4}) = \frac{2}{2}

General solutions for

sin (x + \frac{π}{4}) = \frac{2}{2}

x + \frac{π}{4} = \frac{π}{4} + 2 πn, x + \frac{π}{4} = \frac{3 π}{4} + 2 πn

Solve

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

Solve

x + \frac{π}{4} = \frac{3 π}{4} + 2 πn : x = 2 πn + \frac{π}{2}

x = 2 πn, x = 2 πn + \frac{π}{2}

5 cos (x) - 5 = 0

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cot (x - \frac{π}{2}) + 1 = 0

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