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

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

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-2cot(θ)=-1-cot^2(θ)

- 2 cot (θ) = - 1 - cot^{2} (θ)

θ = \frac{π}{4} + πn

Solution steps

- 2 cot (θ) = - 1 - cot^{2} (θ)

Solve by substitution

cot (θ) = 1

cot (θ) = 1 : θ = \frac{π}{4} + πn

Combine all the solutions

θ = \frac{π}{4} + πn

- cos^{2} (x) - sin (x) - 1 = 0

- 8 cos^{2} (x) + 1 = 4 sin^{2} (x) - 8 cos (x)

\frac{1 + csc ( y )}{cot ( y ) + cos ( y )} = csc (y)

2 = sin (10 x)

cos (2 x) = \frac{( 2 k - 8 )}{9}

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