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

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

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

3 = 23 - 3 cot (x)

x = \frac{π}{3} + πn

Degrees

x = 6 0^{\circ} + 18 0^{\circ} n

Solution steps

3 = 23 - 3 cot (x)

Switch sides

23 - 3 cot (x) = 3

Move

23

to the right side

23 - 3 cot (x) = 3

Subtract

23

from both sides

23 - 3 cot (x) - 23 = 3 - 23

Simplify

23 - 3 cot (x) - 23 = 3 - 23

Simplify

23 - 3 cot (x) - 23 : - 3 cot (x)

23 - 3 cot (x) - 23

Add similar elements:

23 - 23 = 0

= - 3 cot (x)

Simplify

3 - 23 : - 3

3 - 23

Add similar elements:

3 - 23 = - 3

= - 3

- 3 cot (x) = - 3

- 3 cot (x) = - 3

- 3 cot (x) = - 3

Divide both sides by

- 3

- 3 cot (x) = - 3

Divide both sides by

- 3

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

Simplify

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{π}{3} + πn

x = \frac{π}{3} + πn

2 tan^{2} (θ) - tan (θ) = 3

3 cos (2 θ) - cos (θ) + 1 = 0

170 = \frac{9 0 ^{2}}{16} sin (x) cos (x)

3 cos (x) - 2 sin^{2} (x) = 0

sin (x - \frac{π}{3}) = 0

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