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

The general solution for sin(x)-cos(x)=-1 is x=2pin+(3pi)/2 ,x=2pin+2pi

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sin(x)-cos(x)=-1

sin (x) - cos (x) = - 1

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

Solution steps

sin (x) - cos (x) = - 1

Rewrite using trig identities

2 sin (x - \frac{π}{4}) = - 1

Divide both sides by

2

sin (x - \frac{π}{4}) = - \frac{2}{2}

General solutions for

sin (x - \frac{π}{4}) = - \frac{2}{2}

x - \frac{π}{4} = \frac{5 π}{4} + 2 πn, x - \frac{π}{4} = \frac{7 π}{4} + 2 πn

Solve

x - \frac{π}{4} = \frac{5 π}{4} + 2 πn : x = 2 πn + \frac{3 π}{2}

Solve

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

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

4 cos (θ) + 22 = 0

tan^{2} (x) + 1 = 0

sec (θ) = \frac{- 2 3}{3}

2 sin^{2} (x) - 3 sin (x) + 1 = 0, 0 \leq x \leq 2 π

16 sin^{2} (x) - 1 = 0

What is the general solution for sin(x)-cos(x)=-1 ?
The general solution for sin(x)-cos(x)=-1 is x=2pin+(3pi)/2 ,x=2pin+2pi