What is the general solution for 12cot^2(x)-cot(x)=1 ?

The general solution for 12cot^2(x)-cot(x)=1 is x=1.24904…+pin,x=1.81577…+pin

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12cot^2(x)-cot(x)=1

12 cot^{2} (x) - cot (x) = 1

x = 1.24904 \dots + πn, x = 1.81577 \dots + πn

Solution steps

12 cot^{2} (x) - cot (x) = 1

Solve by substitution

cot (x) = \frac{1}{3}, cot (x) = - \frac{1}{4}

cot (x) = \frac{1}{3} : x = arccot (\frac{1}{3}) + πn

cot (x) = - \frac{1}{4} : x = arccot (- \frac{1}{4}) + πn

Combine all the solutions

x = arccot (\frac{1}{3}) + πn, x = arccot (- \frac{1}{4}) + πn

Show solutions in decimal form

x = 1.24904 \dots + πn, x = 1.81577 \dots + πn

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What is the general solution for 12cot^2(x)-cot(x)=1 ?
The general solution for 12cot^2(x)-cot(x)=1 is x=1.24904…+pin,x=1.81577…+pin