What is the general solution for csc^2(x)+4csc(x)+4=0 ?

The general solution for csc^2(x)+4csc(x)+4=0 is x=(7pi)/6+2pin,x=(11pi)/6+2pin

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csc^2(x)+4csc(x)+4=0

csc^{2} (x) + 4 csc (x) + 4 = 0

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

Solution steps

csc^{2} (x) + 4 csc (x) + 4 = 0

Solve by substitution

csc (x) = - 2

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

Combine all the solutions

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

6 sin^{2} (x) - cos (x) - 4 = 0

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

4 cos (x) + 1 = 3

y, x = sin (y)

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

What is the general solution for csc^2(x)+4csc(x)+4=0 ?
The general solution for csc^2(x)+4csc(x)+4=0 is x=(7pi)/6+2pin,x=(11pi)/6+2pin