What is the general solution for 4cot(x)+1=1+2cot(x) ?

The general solution for 4cot(x)+1=1+2cot(x) is x= pi/2+pin

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4cot(x)+1=1+2cot(x)

4 cot (x) + 1 = 1 + 2 cot (x)

x = \frac{π}{2} + πn

Degrees

x = 9 0^{\circ} + 18 0^{\circ} n

Solution steps

4 cot (x) + 1 = 1 + 2 cot (x)

Solve by substitution

4 cot (x) + 1 = 1 + 2 cot (x)

Let:

cot (x) = u

4 u + 1 = 1 + 2 u

4 u + 1 = 1 + 2 u : u = 0

4 u + 1 = 1 + 2 u

Subtract

1

from both sides

4 u + 1 - 1 = 1 + 2 u - 1

Simplify

4 u = 2 u

Move

2 u

to the left side

4 u = 2 u

Subtract

2 u

from both sides

4 u - 2 u = 2 u - 2 u

Simplify

2 u = 0

2 u = 0

Divide both sides by

2

2 u = 0

Divide both sides by

2

\frac{2 u}{2} = \frac{0}{2}

Simplify

u = 0

u = 0

Substitute back

u = cot (x)

cot (x) = 0

cot (x) = 0

cot (x) = 0 : x = \frac{π}{2} + πn

cot (x) = 0

General solutions for

cot (x) = 0

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}{2} + πn

x = \frac{π}{2} + πn

Combine all the solutions

x = \frac{π}{2} + πn

What is the general solution for 4cot(x)+1=1+2cot(x) ?
The general solution for 4cot(x)+1=1+2cot(x) is x= pi/2+pin