What is the general solution for cot(x-pi/4)=-1 ?

The general solution for cot(x-pi/4)=-1 is x=pin+pi

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cot(x-pi/4)=-1

cot (x - \frac{π}{4}) = - 1

x = πn + π

Degrees

x = 18 0^{\circ} + 18 0^{\circ} n

Solution steps

cot (x - \frac{π}{4}) = - 1

General solutions for

cot (x - \frac{π}{4}) = - 1

cot (x)

periodicity table with

πn

cycle:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} cot (x) \mp \infty 31 \frac{3}{3} 0 - \frac{3}{3} - 1 - 3

x - \frac{π}{4} = \frac{3 π}{4} + πn

x - \frac{π}{4} = \frac{3 π}{4} + πn

Solve

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

x - \frac{π}{4} = \frac{3 π}{4} + πn

Move

\frac{π}{4}

to the right side

x - \frac{π}{4} = \frac{3 π}{4} + πn

Add

\frac{π}{4}

to both sides

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

Simplify

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

Simplify

x - \frac{π}{4} + \frac{π}{4} : x

x - \frac{π}{4} + \frac{π}{4}

Add similar elements:

- \frac{π}{4} + \frac{π}{4} = 0

= x

Simplify

\frac{3 π}{4} + πn + \frac{π}{4} : πn + π

\frac{3 π}{4} + πn + \frac{π}{4}

Group like terms

= πn + \frac{π}{4} + \frac{3 π}{4}

Combine the fractions

\frac{π}{4} + \frac{3 π}{4} : π

Apply rule

\frac{a}{c} \pm \frac{b}{c} = \frac{a \pm b}{c}

= \frac{π + 3 π}{4}

Add similar elements:

π + 3 π = 4 π

= \frac{4 π}{4}

Divide the numbers:

\frac{4}{4} = 1

= π

= πn + π

x = πn + π

x = πn + π

x = πn + π

x = πn + π

3 cos (θ) + 1 = 1

sin (θ) = 3

2 cos (x) csc (x) = 2 cos (x)

- 2 cos^{2} (x) = 3 cos (x) + 1

1 + sec (x) = 3

What is the general solution for cot(x-pi/4)=-1 ?
The general solution for cot(x-pi/4)=-1 is x=pin+pi