What is the general solution for cot^2(θ)+4csc(θ)=-5 ?

The general solution for cot^2(θ)+4csc(θ)=-5 is θ=(7pi)/6+2pin,θ=(11pi)/6+2pin

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cot^2(θ)+4csc(θ)=-5

cot^{2} (θ) + 4 csc (θ) = - 5

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

Solution steps

cot^{2} (θ) + 4 csc (θ) = - 5

Subtract

- 5

from both sides

cot^{2} (θ) + 4 csc (θ) + 5 = 0

Rewrite using trig identities

4 + csc^{2} (θ) + 4 csc (θ) = 0

Solve by substitution

csc (θ) = - 2

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

Combine all the solutions

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

10 sin (a) + 7 sin (a) + 1 sin (a) + 8 sin (a) = 48

2 cos^{2} (θ) + 7 sin (θ) = 5

\frac{2 3}{3} = sec (θ)

4 (sin (x))^{2} - 15 sin (x) - 4 = 0

1 + sin (θ) = 1 + sin (- θ)

What is the general solution for cot^2(θ)+4csc(θ)=-5 ?
The general solution for cot^2(θ)+4csc(θ)=-5 is θ=(7pi)/6+2pin,θ=(11pi)/6+2pin