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

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

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-cos(θ)+sin(θ)=1

- cos (θ) + sin (θ) = 1

θ = \frac{π}{2} + 2 πn, θ = 2 πn + π

Solution steps

- cos (θ) + sin (θ) = 1

Rewrite using trig identities

2 sin (θ - \frac{π}{4}) = 1

Divide both sides by

2

sin (θ - \frac{π}{4}) = \frac{2}{2}

General solutions for

sin (θ - \frac{π}{4}) = \frac{2}{2}

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

Solve

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

Solve

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

θ = \frac{π}{2} + 2 πn, θ = 2 πn + π

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

(cot (θ) + 1) (sin (θ) - 1) = 0

sec (2 x) = tan (2 x) + 1

sec^{2} (x) + 3 sec (x) + 2 = 0

3 sin (x) cos (x) - 2 cos (x) = 0

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