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

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

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sin(x)-cos(x)=sqrt(2)

sin (x) - cos (x) = 2

x = 2 πn + \frac{3 π}{4}

Solution steps

sin (x) - cos (x) = 2

Rewrite using trig identities

2 sin (x - \frac{π}{4}) = 2

Divide both sides by

2

sin (x - \frac{π}{4}) = 1

General solutions for

sin (x - \frac{π}{4}) = 1

x - \frac{π}{4} = \frac{π}{2} + 2 πn

Solve

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

x = 2 πn + \frac{3 π}{4}

sin (x) = \frac{3}{2}, 0 \leq x \leq 2 π

2 sin (θ) = 0

- 2 cos (x) = 0

3 cos (θ) + cos (2 θ) = - 2

15 sin (x) + 7 = sin (x)

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