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

The general solution for cos(x)-sin(x)=sqrt(2) is x=(7pi)/4+2pin

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

cos (x) - sin (x) = 2

x = \frac{7 π}{4} + 2 πn

Solution steps

cos (x) - sin (x) = 2

Subtract

2

from both sides

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

Rewrite using trig identities

- 2 - 2 sin (\frac{4 x - π}{4}) = 0

Move

2

to the right side

- 2 sin (\frac{4 x - π}{4}) = 2

Divide both sides by

- 2

sin (\frac{4 x - π}{4}) = - 1

General solutions for

sin (\frac{4 x - π}{4}) = - 1

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

Solve

\frac{4 x - π}{4} = \frac{3 π}{2} + 2 πn : x = \frac{7 π}{4} + 2 πn

x = \frac{7 π}{4} + 2 πn

cot (θ) = (5.8473)

6 = 2 + 5 arctan (\frac{x}{2})

tan^{2} (θ) - 2 sec (θ) = 2

- sin (B) - 4 = 3 sin (B) - 5

cos^{2} (x) - 7 cos (x) - 1 = 0

What is the general solution for cos(x)-sin(x)=sqrt(2) ?
The general solution for cos(x)-sin(x)=sqrt(2) is x=(7pi)/4+2pin