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

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

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

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

No Solution for x \in R

Solution steps

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

Subtract

- csc^{2} (x)

from both sides

cot (x) + csc^{2} (x) = 0

Rewrite using trig identities

1 + cot (x) + cot^{2} (x) = 0

Solve by substitution

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

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

No Solution

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

No Solution

Combine all the solutions

No Solution for x \in R

3 cos^{2} (θ) + 4 cos (θ) - 4 = 0

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

2 sin (x) cos (x) = 3 sin (x)

sin^{2} (x) = sin (2 x)

sin (5 x + 50) = cos (4 x - 23)

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