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

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

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

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

x = \frac{π}{2} + 2 πn, x = 2 πn + π

Solution steps

- cos (x) + sin (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 = \frac{π}{2} + 2 πn

Solve

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

x = \frac{π}{2} + 2 πn, x = 2 πn + π

sin (2 x) = 2 sin (x)

cos (2 x - \frac{π}{4}) = 0

- cos (θ) + sin (θ) = 1

15 tan^{3} (x) = 5 tan (x)

(cot (θ) + 1) (sin (θ) - 1) = 0

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