What is the general solution for -12cot(x)-4sqrt(3)=0 ?

The general solution for -12cot(x)-4sqrt(3)=0 is x=(2pi)/3+pin

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-12cot(x)-4sqrt(3)=0

- 12 cot (x) - 43 = 0

x = \frac{2 π}{3} + πn

Degrees

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

Solution steps

- 12 cot (x) - 43 = 0

Move

43

to the right side

- 12 cot (x) - 43 = 0

Add

43

to both sides

- 12 cot (x) - 43 + 43 = 0 + 43

Simplify

- 12 cot (x) = 43

- 12 cot (x) = 43

Divide both sides by

- 12

- 12 cot (x) = 43

Divide both sides by

- 12

\frac{- 12 cot ( x )}{- 12} = \frac{4 3}{- 12}

Simplify

\frac{- 12 cot ( x )}{- 12} = \frac{4 3}{- 12}

Simplify

\frac{- 12 cot ( x )}{- 12} : cot (x)

\frac{- 12 cot ( x )}{- 12}

Apply the fraction rule:

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

= \frac{12 cot ( x )}{12}

Divide the numbers:

\frac{12}{12} = 1

= cot (x)

Simplify

\frac{4 3}{- 12} : - \frac{3}{3}

\frac{4 3}{- 12}

Apply the fraction rule:

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

= - \frac{4 3}{12}

Cancel the common factor:

4

= - \frac{3}{3}

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

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

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

General solutions for

cot (x) = - \frac{3}{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{2 π}{3} + πn

x = \frac{2 π}{3} + πn

3 sin^{2} (t) = 2 cos (t) sin (t)

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

cos (x) (tan (x) + \frac{cos ( x )}{sin ( x )}) = 2

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

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

What is the general solution for -12cot(x)-4sqrt(3)=0 ?
The general solution for -12cot(x)-4sqrt(3)=0 is x=(2pi)/3+pin