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

The general solution for cot^2(x)=-cot(x) is x= pi/2+pin,x=(3pi)/4+pin

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

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

x = \frac{π}{2} + πn, x = \frac{3 π}{4} + πn

Solution steps

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

Solve by substitution

cot (x) = 0, cot (x) = - 1

cot (x) = 0 : x = \frac{π}{2} + πn

cot (x) = - 1 : x = \frac{3 π}{4} + πn

Combine all the solutions

x = \frac{π}{2} + πn, x = \frac{3 π}{4} + πn

2 cos (θ) = - 3, 0 \leq θ < 2 π

2 cos (3 θ) = - 3, 0 \leq θ \leq 2 π

csc (θ) = 10

cos (2 x) = \frac{2}{2}, (0, 2 π)

tan (2 x) = 2 tan (x)

What is the general solution for cot^2(x)=-cot(x) ?
The general solution for cot^2(x)=-cot(x) is x= pi/2+pin,x=(3pi)/4+pin