What is the general solution for 5cot(x)-5=0 ?

The general solution for 5cot(x)-5=0 is x= pi/4+pin

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5cot(x)-5=0

5 cot (x) - 5 = 0

x = \frac{π}{4} + πn

Degrees

x = 4 5^{\circ} + 18 0^{\circ} n

Solution steps

5 cot (x) - 5 = 0

Move

5

to the right side

5 cot (x) - 5 = 0

Add

5

to both sides

5 cot (x) - 5 + 5 = 0 + 5

Simplify

5 cot (x) = 5

5 cot (x) = 5

Divide both sides by

5

5 cot (x) = 5

Divide both sides by

5

\frac{5 cot ( x )}{5} = \frac{5}{5}

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{π}{4} + πn

x = \frac{π}{4} + πn

2 - \frac{1}{2} sin (3 x + 330) = \frac{8 - 3}{4}

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

sin (x) = \frac{20}{29}

7 cos^{2} (x) - 2 = 0

tan (\frac{θ}{2} + \frac{π}{6}) = - 1

What is the general solution for 5cot(x)-5=0 ?
The general solution for 5cot(x)-5=0 is x= pi/4+pin