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

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

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

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

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

Solution steps

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

Rewrite using trig identities

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

cos (2 x) + cos (x) - 1 = 0

cos (2 x) - 1 = - sin (2 x)

5 sin (x) = 3 + 3 sin (x)

cos (a) = 0.3

5 + 3 tan (x) = 4

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