What is the general solution for sin(x)-cos(x)=sqrt(3/2) ?

The general solution for sin(x)-cos(x)=sqrt(3/2) is x=2pin+(7pi)/(12),x=2pin+(11pi)/(12)

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sin(x)-cos(x)=sqrt(3/2)

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

x = 2 πn + \frac{7 π}{12}, x = 2 πn + \frac{11 π}{12}

Solution steps

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

Rewrite using trig identities

2 sin (x - \frac{π}{4}) = \frac{3}{2}

Divide both sides by

2

sin (x - \frac{π}{4}) = \frac{3}{2}

General solutions for

sin (x - \frac{π}{4}) = \frac{3}{2}

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

Solve

x - \frac{π}{4} = \frac{π}{3} + 2 πn : x = 2 πn + \frac{7 π}{12}

Solve

x - \frac{π}{4} = \frac{2 π}{3} + 2 πn : x = 2 πn + \frac{11 π}{12}

x = 2 πn + \frac{7 π}{12}, x = 2 πn + \frac{11 π}{12}

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

csc (x) = \frac{7}{4}

2 - 4 cos (A) = 0

6 cos (6 x) = 3

x, sin (x) cos (y) = 0

What is the general solution for sin(x)-cos(x)=sqrt(3/2) ?
The general solution for sin(x)-cos(x)=sqrt(3/2) is x=2pin+(7pi)/(12),x=2pin+(11pi)/(12)