What is the general solution for csc^2(x)-csc(x)-2=0,-pi<= x<= pi ?

The general solution for csc^2(x)-csc(x)-2=0,-pi<= x<= pi is x= pi/6 ,x=(5pi)/6 ,x=-pi/2

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csc^2(x)-csc(x)-2=0,-pi<= x<= pi

csc^{2} (x) - csc (x) - 2 = 0, - π \leq x \leq π

x = \frac{π}{6}, x = \frac{5 π}{6}, x = - \frac{π}{2}

Solution steps

csc^{2} (x) - csc (x) - 2 = 0, - π \leq x \leq π

Solve by substitution

csc (x) = 2, csc (x) = - 1

csc (x) = 2, - π \leq x \leq π : x = \frac{π}{6}, x = \frac{5 π}{6}

csc (x) = - 1, - π \leq x \leq π : x = - \frac{π}{2}

Combine all the solutions

x = \frac{π}{6}, x = \frac{5 π}{6}, x = - \frac{π}{2}

θ, r = v cos (θ) (\frac{2 v sin ( θ )}{g})

5 = 5 + 4 cos (θ)

cos (θ) = - 0.47

1 + tan^{2} (x) cos (x) = sec (x)

sec (θ) = \frac{6}{2}

What is the general solution for csc^2(x)-csc(x)-2=0,-pi<= x<= pi ?
The general solution for csc^2(x)-csc(x)-2=0,-pi<= x<= pi is x= pi/6 ,x=(5pi)/6 ,x=-pi/2