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

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

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

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

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

Solution steps

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

Rewrite using trig identities

2 sin (x - \frac{π}{4}) = \frac{2}{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}

2 cos (x) = 7 - \frac{3}{cos ( x )}

- sin (x) + 2 = 0

csc (x) = - \frac{9}{7}, tan (x) > 0

sin (x) = \frac{12}{37}

tan (θ) = \frac{- 2 3}{2}

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