What is the general solution for 6=cot^2(x)+8cot(x) ?

The general solution for 6=cot^2(x)+8cot(x) is x=0.96653…+pin,x=3.02702…+pin

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6=cot^2(x)+8cot(x)

6 = cot^{2} (x) + 8 cot (x)

x = 0.96653 \dots + πn, x = 3.02702 \dots + πn

Solution steps

6 = cot^{2} (x) + 8 cot (x)

Switch sides

cot^{2} (x) + 8 cot (x) = 6

Solve by substitution

cot (x) = - 4 + 22, cot (x) = - 4 - 22

cot (x) = - 4 + 22 : x = arccot (- 4 + 22) + πn

cot (x) = - 4 - 22 : x = arccot (- 4 - 22) + πn

Combine all the solutions

x = arccot (- 4 + 22) + πn, x = arccot (- 4 - 22) + πn

Show solutions in decimal form

x = 0.96653 \dots + πn, x = 3.02702 \dots + πn

sin^{2} (\frac{2 x}{3}) - 1 = 0

5 sin (x) = 2 + sin (x)

- 3 = 4 - 2 arctan (\frac{4 - 2 - C}{4 - C})

cos^{2} (x) + \frac{11}{2} cos (x) = 3 cos (x) - 1

23 sin (4 θ) = 3

What is the general solution for 6=cot^2(x)+8cot(x) ?
The general solution for 6=cot^2(x)+8cot(x) is x=0.96653…+pin,x=3.02702…+pin