What is the general solution for sin(x)-cos(x)= 1/(sqrt(2)) ?

The general solution for sin(x)-cos(x)= 1/(sqrt(2)) is x=2pin+(5pi)/(12),x=2pin+(13pi)/(12)

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sin(x)-cos(x)= 1/(sqrt(2))

sin (x) - cos (x) = \frac{1}{2}

x = 2 πn + \frac{5 π}{12}, x = 2 πn + \frac{13 π}{12}

Solution steps

sin (x) - cos (x) = \frac{1}{2}

Rewrite using trig identities

2 sin (x - \frac{π}{4}) = \frac{1}{2}

Divide both sides by

2

sin (x - \frac{π}{4}) = \frac{1}{2}

General solutions for

sin (x - \frac{π}{4}) = \frac{1}{2}

x - \frac{π}{4} = \frac{π}{6} + 2 πn, x - \frac{π}{4} = \frac{5 π}{6} + 2 πn

Solve

x - \frac{π}{4} = \frac{π}{6} + 2 πn : x = 2 πn + \frac{5 π}{12}

Solve

x - \frac{π}{4} = \frac{5 π}{6} + 2 πn : x = 2 πn + \frac{13 π}{12}

x = 2 πn + \frac{5 π}{12}, x = 2 πn + \frac{13 π}{12}

cos (x) = \frac{6}{15}

arccos (x) = 90

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

sin (θ) = \frac{7}{12}

3 cos (2 x) + 2 sin^{2} (x) = 2

What is the general solution for sin(x)-cos(x)= 1/(sqrt(2)) ?
The general solution for sin(x)-cos(x)= 1/(sqrt(2)) is x=2pin+(5pi)/(12),x=2pin+(13pi)/(12)