What is the general solution for 12csc^2(θ)-csc(θ)-1=0 ?

The general solution for 12csc^2(θ)-csc(θ)-1=0 is No Solution for θ\in\mathbb{R}

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12csc^2(θ)-csc(θ)-1=0

12 csc^{2} (θ) - csc (θ) - 1 = 0

No Solution for θ \in R

Solution steps

12 csc^{2} (θ) - csc (θ) - 1 = 0

Solve by substitution

csc (θ) = \frac{1}{3}, csc (θ) = - \frac{1}{4}

csc (θ) = \frac{1}{3} :

No Solution

csc (θ) = - \frac{1}{4} :

No Solution

Combine all the solutions

No Solution for θ \in R

2 cos (2 θ) - 4 cos (θ) + 2 = - 1

cos (a) = \frac{1}{sin ( a )}

sin (a) = cos (a)

tan (a) = 2.0503

4 sin (x) = 3 csc (x) - 4

What is the general solution for 12csc^2(θ)-csc(θ)-1=0 ?
The general solution for 12csc^2(θ)-csc(θ)-1=0 is No Solution for θ\in\mathbb{R}