What is the general solution for 4cot(x)+2=6 ?

The general solution for 4cot(x)+2=6 is x= pi/4+pin

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4cot(x)+2=6

4 cot (x) + 2 = 6

x = \frac{π}{4} + πn

Degrees

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

Solution steps

4 cot (x) + 2 = 6

Move

2

to the right side

4 cot (x) + 2 = 6

Subtract

2

from both sides

4 cot (x) + 2 - 2 = 6 - 2

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{π}{4} + πn

x = \frac{π}{4} + πn

4 sin^{2} (θ) - 4 = - 3

2 sin (x) = sin^{2} (x)

cot^{2} (x) = - 3 cot (x)

tan (θ) = \frac{cos ( θ )}{sin ( θ )}

sin (θ) + 2 sin^{2} (θ) = 0

What is the general solution for 4cot(x)+2=6 ?
The general solution for 4cot(x)+2=6 is x= pi/4+pin