What is the general solution for 4cot(x)+5=1 ?

The general solution for 4cot(x)+5=1 is x=(3pi)/4+pin

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4cot(x)+5=1

4 cot (x) + 5 = 1

x = \frac{3 π}{4} + πn

Degrees

x = 13 5^{\circ} + 18 0^{\circ} n

Solution steps

4 cot (x) + 5 = 1

Move

5

to the right side

4 cot (x) + 5 = 1

Subtract

5

from both sides

4 cot (x) + 5 - 5 = 1 - 5

Simplify

4 cot (x) = - 4

4 cot (x) = - 4

Divide both sides by

4

4 cot (x) = - 4

Divide both sides by

4

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

Simplify

cot (x) = - 1

cot (x) = - 1

General solutions for

cot (x) = - 1

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{3 π}{4} + πn

x = \frac{3 π}{4} + πn

What is the general solution for 4cot(x)+5=1 ?
The general solution for 4cot(x)+5=1 is x=(3pi)/4+pin