What is the general solution for -2cot(x)+1=2sqrt(3)+1 ?

The general solution for -2cot(x)+1=2sqrt(3)+1 is x=(5pi)/6+pin

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-2cot(x)+1=2sqrt(3)+1

- 2 cot (x) + 1 = 23 + 1

x = \frac{5 π}{6} + πn

Degrees

x = 15 0^{\circ} + 18 0^{\circ} n

Solution steps

- 2 cot (x) + 1 = 23 + 1

Subtract

1

from both sides

- 2 cot (x) + 1 - 1 = 23 + 1 - 1

Simplify

- 2 cot (x) = 23

Divide both sides by

- 2

- 2 cot (x) = 23

Divide both sides by

- 2

\frac{- 2 cot ( x )}{- 2} = \frac{2 3}{- 2}

Simplify

\frac{- 2 cot ( x )}{- 2} = \frac{2 3}{- 2}

Simplify

\frac{- 2 cot ( x )}{- 2} : cot (x)

\frac{- 2 cot ( x )}{- 2}

Apply the fraction rule:

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

= \frac{2 cot ( x )}{2}

Divide the numbers:

\frac{2}{2} = 1

= cot (x)

Simplify

\frac{2 3}{- 2} : - 3

\frac{2 3}{- 2}

Apply the fraction rule:

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

= - \frac{2 3}{2}

Divide the numbers:

\frac{2}{2} = 1

= - 3

cot (x) = - 3

cot (x) = - 3

cot (x) = - 3

General solutions for

cot (x) = - 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} + πn

x = \frac{5 π}{6} + πn

What is the general solution for -2cot(x)+1=2sqrt(3)+1 ?
The general solution for -2cot(x)+1=2sqrt(3)+1 is x=(5pi)/6+pin