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

The general solution for 4(cot(x)-sqrt(3))=cot(x)-sqrt(3) is x= pi/6+pin

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

Solution

4 (cot (x) - 3) = cot (x) - 3

Solution

x = \frac{π}{6} + πn

Degrees

x = 3 0^{\circ} + 18 0^{\circ} n

Solution steps

4 (cot (x) - 3) = cot (x) - 3

Solve by substitution

4 (cot (x) - 3) = cot (x) - 3

Let:

cot (x) = u

4 (u - 3) = u - 3

4 (u - 3) = u - 3 : u = 3

4 (u - 3) = u - 3

Expand

4 (u - 3) : 4 u - 43

4 (u - 3)

Apply the distributive law:

a (b - c) = ab - a c

a = 4, b = u, c = 3

= 4 u - 43

4 u - 43 = u - 3

Move

43

to the right side

4 u - 43 = u - 3

Add

43

to both sides

4 u - 43 + 43 = u - 3 + 43

Simplify

4 u - 43 + 43 = u - 3 + 43

Simplify

4 u - 43 + 43 : 4 u

4 u - 43 + 43

Add similar elements:

- 43 + 43 = 0

= 4 u

Simplify

u - 3 + 43 : u + 33

u - 3 + 43

Add similar elements:

- 3 + 43 = 33

= u + 33

4 u = u + 33

4 u = u + 33

4 u = u + 33

Move

u

to the left side

4 u = u + 33

Subtract

u

from both sides

4 u - u = u + 33 - u

Simplify

3 u = 33

3 u = 33

Divide both sides by

3

3 u = 33

Divide both sides by

3

\frac{3 u}{3} = \frac{3 3}{3}

Simplify

u = 3

u = 3

Substitute back

u = cot (x)

cot (x) = 3

cot (x) = 3

cot (x) = 3 : x = \frac{π}{6} + πn

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{π}{6} + πn

x = \frac{π}{6} + πn

Combine all the solutions

x = \frac{π}{6} + πn

Popular Examples

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5 sec (x) = 2 sec (x) + 7

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sin (x) = (\frac{5}{9})

cos(θ)=(sqrt(2))/2 ,sin(θ)=-(sqrt(2))/2

cos (θ) = \frac{2}{2}, sin (θ) = - \frac{2}{2}

cos(θ)=(198.36)/(229.4)

cos (θ) = \frac{198.36}{229.4}

(cos(x)-1)(tan(x)-1)=0

(cos (x) - 1) (tan (x) - 1) = 0

Frequently Asked Questions (FAQ)

What is the general solution for 4(cot(x)-sqrt(3))=cot(x)-sqrt(3) ?
The general solution for 4(cot(x)-sqrt(3))=cot(x)-sqrt(3) is x= pi/6+pin