What is the general solution for sin(x)-cos(x)-1/(sqrt(2))=0 ?

The general solution for sin(x)-cos(x)-1/(sqrt(2))=0 is x=2pin+(5pi)/(12),x=2pin+(13pi)/(12)

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sin(x)-cos(x)-1/(sqrt(2))=0

sin (x) - cos (x) - \frac{1}{2} = 0

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

Solution steps

sin (x) - cos (x) - \frac{1}{2} = 0

Rewrite using trig identities

- \frac{1}{2} + 2 sin (x - \frac{π}{4}) = 0

Move

\frac{1}{2}

to the right side

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}

cos^{2} (θ) = \frac{49}{64}

sec^{2} (θ) = 1 - tan (θ)

cos^{2} (x) = - 0.267

sin (x - 4) = cos (9 x + 4)

x, 0 = - 2 sin (x) - 4 cos (2 x)

What is the general solution for sin(x)-cos(x)-1/(sqrt(2))=0 ?
The general solution for sin(x)-cos(x)-1/(sqrt(2))=0 is x=2pin+(5pi)/(12),x=2pin+(13pi)/(12)