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

The general solution for sin(2x)-cos(2x)=sqrt(2) is x=pin+(3pi)/8

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

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

x = πn + \frac{3 π}{8}

Solution steps

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

Rewrite using trig identities

2 sin (2 x - \frac{π}{4}) = 2

Divide both sides by

2

sin (2 x - \frac{π}{4}) = 1

General solutions for

sin (2 x - \frac{π}{4}) = 1

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

Solve

2 x - \frac{π}{4} = \frac{π}{2} + 2 πn : x = πn + \frac{3 π}{8}

x = πn + \frac{3 π}{8}

5 tan^{2} (x) - tan (x) = 0

3 tan (2 x) - 3 = 0

csc^{2} (x) = 3 cot (x) + 5

7^{2} + 2 5^{2} - 2 (7) (25) cos (x) = 2 4^{2}

tan (x) = 0.015

What is the general solution for sin(2x)-cos(2x)=sqrt(2) ?
The general solution for sin(2x)-cos(2x)=sqrt(2) is x=pin+(3pi)/8