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

The general solution for -cot^2(x)=1+2cot(x) is x=(3pi)/4+pin

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

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

x = \frac{3 π}{4} + πn

Solution steps

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

Solve by substitution

cot (x) = - 1

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

Combine all the solutions

x = \frac{3 π}{4} + πn

6 sec (2 x) + 3 tan (2 x) - 9 = 0

3 cos^{2} (x) + 3 = 4, 0 \leq x < 2 π

tan (2 x) = 3

3 = tan (x)

sin (x) tan (x) = 3 sin (x)

What is the general solution for -cot^2(x)=1+2cot(x) ?
The general solution for -cot^2(x)=1+2cot(x) is x=(3pi)/4+pin