What is the general solution for cot(x+(5pi)/6)=sqrt(3) ?

The general solution for cot(x+(5pi)/6)=sqrt(3) is x=pin-(2pi)/3

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cot(x+(5pi)/6)=sqrt(3)

cot (x + \frac{5 π}{6}) = 3

x = πn - \frac{2 π}{3}

Degrees

x = - 12 0^{\circ} + 18 0^{\circ} n

Solution steps

cot (x + \frac{5 π}{6}) = 3

General solutions for

cot (x + \frac{5 π}{6}) = 3

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{5 π}{6} = \frac{π}{6} + πn

x + \frac{5 π}{6} = \frac{π}{6} + πn

Solve

x + \frac{5 π}{6} = \frac{π}{6} + πn : x = πn - \frac{2 π}{3}

x + \frac{5 π}{6} = \frac{π}{6} + πn

Move

\frac{5 π}{6}

to the right side

x + \frac{5 π}{6} = \frac{π}{6} + πn

Subtract

\frac{5 π}{6}

from both sides

x + \frac{5 π}{6} - \frac{5 π}{6} = \frac{π}{6} + πn - \frac{5 π}{6}

Simplify

x + \frac{5 π}{6} - \frac{5 π}{6} = \frac{π}{6} + πn - \frac{5 π}{6}

Simplify

x + \frac{5 π}{6} - \frac{5 π}{6} : x

x + \frac{5 π}{6} - \frac{5 π}{6}

Add similar elements:

\frac{5 π}{6} - \frac{5 π}{6} = 0

= x

Simplify

\frac{π}{6} + πn - \frac{5 π}{6} : πn - \frac{2 π}{3}

\frac{π}{6} + πn - \frac{5 π}{6}

Group like terms

= πn + \frac{π}{6} - \frac{5 π}{6}

Combine the fractions

\frac{π}{6} - \frac{5 π}{6} : - \frac{2 π}{3}

Apply rule

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

= \frac{π - 5 π}{6}

Add similar elements:

π - 5 π = - 4 π

= \frac{- 4 π}{6}

Apply the fraction rule:

\frac{- a}{b} = - \frac{a}{b}

= - \frac{4 π}{6}

Cancel the common factor:

2

= - \frac{2 π}{3}

= πn - \frac{2 π}{3}

x = πn - \frac{2 π}{3}

x = πn - \frac{2 π}{3}

x = πn - \frac{2 π}{3}

x = πn - \frac{2 π}{3}

What is the general solution for cot(x+(5pi)/6)=sqrt(3) ?
The general solution for cot(x+(5pi)/6)=sqrt(3) is x=pin-(2pi)/3