What is the general solution for 3csc^2(x)-5csc(x)-2=0 ?

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

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3csc^2(x)-5csc(x)-2=0

3 csc^{2} (x) - 5 csc (x) - 2 = 0

x = \frac{π}{6} + 2 πn, x = \frac{5 π}{6} + 2 πn

Solution steps

3 csc^{2} (x) - 5 csc (x) - 2 = 0

Solve by substitution

csc (x) = 2, csc (x) = - \frac{1}{3}

csc (x) = 2 : x = \frac{π}{6} + 2 πn, x = \frac{5 π}{6} + 2 πn

csc (x) = - \frac{1}{3} :

No Solution

Combine all the solutions

x = \frac{π}{6} + 2 πn, x = \frac{5 π}{6} + 2 πn

(cot (x) - 1) (3 tan (x) - 1) = 0

2 sin (x) cos (x) + cos (x) = 0, 0 \leq x \leq 2 π

a, sin (2 a) + 1 = 0.5

\frac{( sin ( 5 x ) )}{( - 1 cos ( 5 x ) )} = 0

sin (x) = cos (4 0^{\circ})

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