What is the general solution for sin(θ)-cos(θ)=sqrt(2) ?

The general solution for sin(θ)-cos(θ)=sqrt(2) is θ=2pin+(3pi)/4

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sin(θ)-cos(θ)=sqrt(2)

sin (θ) - cos (θ) = 2

θ = 2 πn + \frac{3 π}{4}

Solution steps

sin (θ) - cos (θ) = 2

Rewrite using trig identities

2 sin (θ - \frac{π}{4}) = 2

Divide both sides by

2

sin (θ - \frac{π}{4}) = 1

General solutions for

sin (θ - \frac{π}{4}) = 1

θ - \frac{π}{4} = \frac{π}{2} + 2 πn

Solve

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

θ = 2 πn + \frac{3 π}{4}

sin (θ) + 3 cos (θ) = 0

cos (x) + 2 sin (x) cos (x) = 0

3 tan (x) + 3 = 0

(2 sin^{2} (x) - 1) (3 tan^{2} (x) - 1) = 0

sec (x) - 1 = 0

What is the general solution for sin(θ)-cos(θ)=sqrt(2) ?
The general solution for sin(θ)-cos(θ)=sqrt(2) is θ=2pin+(3pi)/4