What is the general solution for 3cot(x)-1=cot^2(x) ?

The general solution for 3cot(x)-1=cot^2(x) is x=0.36486…+pin,x=1.20593…+pin

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3cot(x)-1=cot^2(x)

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

x = 0.36486 \dots + πn, x = 1.20593 \dots + πn

Solution steps

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

Solve by substitution

cot (x) = \frac{3 + 5}{2}, cot (x) = \frac{3 - 5}{2}

cot (x) = \frac{3 + 5}{2} : x = arccot (\frac{3 + 5}{2}) + πn

cot (x) = \frac{3 - 5}{2} : x = arccot (\frac{3 - 5}{2}) + πn

Combine all the solutions

x = arccot (\frac{3 + 5}{2}) + πn, x = arccot (\frac{3 - 5}{2}) + πn

Show solutions in decimal form

x = 0.36486 \dots + πn, x = 1.20593 \dots + πn

sin (x) = - 0.974

sin (x) = - 0.978

cos (t) = \frac{15}{17}

cos (x) = - \frac{3}{2 3}

sec^{2} (x) - 6 sec (x) = 16

What is the general solution for 3cot(x)-1=cot^2(x) ?
The general solution for 3cot(x)-1=cot^2(x) is x=0.36486…+pin,x=1.20593…+pin