What is the general solution for csc^2(θ)+cot(θ)=0 ?

The general solution for csc^2(θ)+cot(θ)=0 is No Solution for θ\in\mathbb{R}

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csc^2(θ)+cot(θ)=0

csc^{2} (θ) + cot (θ) = 0

No Solution for θ \in R

Solution steps

csc^{2} (θ) + cot (θ) = 0

Rewrite using trig identities

1 + cot (θ) + cot^{2} (θ) = 0

Solve by substitution

cot (θ) = - \frac{1}{2} + i \frac{3}{2}, cot (θ) = - \frac{1}{2} - i \frac{3}{2}

cot (θ) = - \frac{1}{2} + i \frac{3}{2} :

No Solution

cot (θ) = - \frac{1}{2} - i \frac{3}{2} :

No Solution

Combine all the solutions

No Solution for θ \in R

sin^{2} (θ) - 2 sin (θ) - 3 = 0

5 tan (θ) - 4 = 0

0 = cos (\frac{x}{2})

3 cos (x) - 1 = cos (2 x)

7 cos^{2} (θ) - 9 = - 9 sin (θ)

What is the general solution for csc^2(θ)+cot(θ)=0 ?
The general solution for csc^2(θ)+cot(θ)=0 is No Solution for θ\in\mathbb{R}