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

The general solution for cot^2(x)-cos^2(x)=-1 is No Solution for x\in\mathbb{R}

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

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

No Solution for x \in R

Solution steps

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

Subtract

- 1

from both sides

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

Rewrite using trig identities

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

Factor

- cos^{2} (x) + csc^{2} (x) : (csc (x) + cos (x)) (csc (x) - cos (x))

(csc (x) + cos (x)) (csc (x) - cos (x)) = 0

Solving each part separately

csc (x) + cos (x) = 0 or csc (x) - cos (x) = 0

csc (x) + cos (x) = 0 :

No Solution

csc (x) - cos (x) = 0 :

No Solution

Combine all the solutions

No Solution for x \in R

sin^{2} (θ) = 2 \cdot sin (θ) + 3

tan (3 x) = 1, - 2 π \leq x \leq 2 π

sin (x) = \frac{- 3}{2}

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

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

What is the general solution for cot^2(x)-cos^2(x)=-1 ?
The general solution for cot^2(x)-cos^2(x)=-1 is No Solution for x\in\mathbb{R}