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

The general solution for csc^2(x)+3csc(x)+2=0 is x=(3pi)/2+2pin,x=(7pi)/6+2pin,x=(11pi)/6+2pin

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csc^2(x)+3csc(x)+2=0

csc^{2} (x) + 3 csc (x) + 2 = 0

x = \frac{3 π}{2} + 2 πn, x = \frac{7 π}{6} + 2 πn, x = \frac{11 π}{6} + 2 πn

Solution steps

csc^{2} (x) + 3 csc (x) + 2 = 0

Solve by substitution

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

csc (x) = - 1 : x = \frac{3 π}{2} + 2 πn

csc (x) = - 2 : x = \frac{7 π}{6} + 2 πn, x = \frac{11 π}{6} + 2 πn

Combine all the solutions

x = \frac{3 π}{2} + 2 πn, x = \frac{7 π}{6} + 2 πn, x = \frac{11 π}{6} + 2 πn

2 sin (x) cos (x) + 2 cos (x) = 0

4.718 tan^{2} (θ) - 13.75 tan (θ) + 8.018 = 0

62 cos (θ) + 1 = 7

sin (x) = 0.48

sin (x) = 0.44

What is the general solution for csc^2(x)+3csc(x)+2=0 ?
The general solution for csc^2(x)+3csc(x)+2=0 is x=(3pi)/2+2pin,x=(7pi)/6+2pin,x=(11pi)/6+2pin