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

The general solution for cos(θ)-sin(θ)=1 is θ=(3pi)/2+2pin,θ=2pi+2pin

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cos(θ)-sin(θ)=1

cos (θ) - sin (θ) = 1

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

Solution steps

cos (θ) - sin (θ) = 1

Subtract

1

from both sides

cos (θ) - sin (θ) - 1 = 0

Rewrite using trig identities

- 1 - 2 sin (\frac{4 θ - π}{4}) = 0

Move

1

to the right side

- 2 sin (\frac{4 θ - π}{4}) = 1

Divide both sides by

- 2

sin (\frac{4 θ - π}{4}) = - \frac{2}{2}

General solutions for

sin (\frac{4 θ - π}{4}) = - \frac{2}{2}

\frac{4 θ - π}{4} = \frac{5 π}{4} + 2 πn, \frac{4 θ - π}{4} = \frac{7 π}{4} + 2 πn

Solve

\frac{4 θ - π}{4} = \frac{5 π}{4} + 2 πn : θ = \frac{3 π}{2} + 2 πn

Solve

\frac{4 θ - π}{4} = \frac{7 π}{4} + 2 πn : θ = 2 π + 2 πn

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

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

3 cot^{2} (x) = 1

cos (θ) = - \frac{5}{13}

4 sec (θ) + 6 = - 2

- 2 sin (x) + cos (2 x) \cdot 2 = 0

What is the general solution for cos(θ)-sin(θ)=1 ?
The general solution for cos(θ)-sin(θ)=1 is θ=(3pi)/2+2pin,θ=2pi+2pin