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

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

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-2cot(θ)=cot^2(θ)+1

- 2 cot (θ) = cot^{2} (θ) + 1

θ = \frac{3 π}{4} + πn

Solution steps

- 2 cot (θ) = cot^{2} (θ) + 1

Solve by substitution

cot (θ) = - 1

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

Combine all the solutions

θ = \frac{3 π}{4} + πn

[sin (4 x) cos (x) - cos (4 x) sin (x)]^{2} = 1

cos (θ) = \frac{202}{331 \cdot 2 33}

5 sin (θ) + 12 cos (θ) = 13

2 - 2 cos^{2} (x) + 3 cos (x) = 0

cot (x) = \frac{5}{12}, π < x < \frac{3 π}{2}

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