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

The general solution for csc^2(x)-csc(x)-2=0,0<= x<= 2pi is x= pi/6 ,x=(5pi)/6 ,x=(3pi)/2

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

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

x = \frac{π}{6}, x = \frac{5 π}{6}, x = \frac{3 π}{2}

Solution steps

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

Solve by substitution

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

csc (x) = 2, 0 \leq x \leq 2 π : x = \frac{π}{6}, x = \frac{5 π}{6}

csc (x) = - 1, 0 \leq x \leq 2 π : x = \frac{3 π}{2}

Combine all the solutions

x = \frac{π}{6}, x = \frac{5 π}{6}, x = \frac{3 π}{2}

sinh (x - 1) = 0

32 cos (x) - 6 sin (x) cos (x) = 0

tan (θ) = - \frac{6}{3}

\frac{sin ( x )}{1 - cos ( x )} = 0

2 sec^{2} (x) - 3 + tan (x) = 0

What is the general solution for csc^2(x)-csc(x)-2=0,0<= x<= 2pi ?
The general solution for csc^2(x)-csc(x)-2=0,0<= x<= 2pi is x= pi/6 ,x=(5pi)/6 ,x=(3pi)/2